Looking for games with unique core mechanics

Majora's Mask: a 3-day timeloop where everything resets when you go back
Katamari: A giant ball gets rolled around and collects stuff forever
Baba Is You: Movable text is rules to the game
Untitled Goose Game: You have to piss people off the right way
Billie Bust Up^[unreleased]: Musicals tell you upcoming platforming challenges
Celeste: every time you die you quickly reset on the same "page"/small tile of map
Splatoon: you shoot at the ground to go faster, hide, and/or win
Odama: real-time tactical wargame pinball
Golf Story: Golf-based fetch quests
Astral Chain: asynchronously control a companion in combat
Okami: paint skills on-screen in combat
Astro Bears: Snake but in 3D
Lovers In A Dangerous Spacetime: Up to 4 players pilot parts of a ship together
Pokemon Ranger: draw circles around monsters to catch them
Viva Pinata: breed pinatas to create new species
Spore: create and evolve a creature
- Oh man, I just want to give a shout out to the Splatoon ink mechanic.
  The game is a competitive arena shooter. That would be pretty uninteresting, but instead of competing for kills or holding objectives, the teams are competing to cover the largest surface area with ink or paint. That's pretty neat. But there's more.
  Every player has a special "squid mode" they can use when standing on ink of their colour. When in squid mode players travel much faster, can travel up walls, and are extremely hard to spot, but can not attack or lay new ink.
  This makes the laying ink in specific areas valuable, as it makes it faster to get from the spawn point to the front faster and easier. It also rewards holding contiguous trails of ink, or conversely, cutting off your opponent's ink trails.
- Majora’s Mask: a 3-day timeloop where everything resets when you go back
  As far as time loop mechanics go, there are some other strong contenders for playing with the concept:
  The Sexy Brutale - you are stuck in a short time loop in which people die, and you need to save them. Successfully saving someone grants you a special power that can be used to try to save others. You have to untangle who and how to save each one and exactly what's going on. You keep the powers between loops, and also start each loop from the last clock you checked in at.
  Deathloop - Arkane stealth shooter stuck in a one day loop. Several locations, different events in each location each day, goal is to arrange the right day so you can kill all your targets in one loop.
  Death Come True - interactive film game. You wake up in a hotel room, and have to figure out what's going on. Loop continues until you die, at which point you wake up in the hotel room again.
  12 Minutes - You come back to your apartment, and unless you change the course of events (or on the first loop, do not touch the controls at all) you will die in less than 12 minutes. Then loop until you understand what's going on.
- Okami plays extremely well on Nintendo Switch with the ability to paint with your fingers on the touch screen
- Katamari Damacy is a great example, built around a very simple but satifying mechanic snd good controls.

Hey, I might have a few for you!
Majesty (Majesty 2 is okay, but lacks the charm of the original, but YMMV) - you run a kingdom full of heroes. The catch? You don't command the heroes. They have their own AI and goals and you have to offer incentives and place the necessary buildings appropriately to both enable and encourage them to do their jobs of saving the kingdom.
Ronin - a stealth/platformer. Combat is turn-based. No, combat is not mechanically separate from the stealth OR the platforming. Relatively short but very fascinating.
Pawnbarian - Roguelike, but movement and combat is done by chess rules.
Exanima. Combat is based entirely around physics/momentum and positioning. It's hard to get the hang of, but is immensely satisfying once you get your "He's starting to believe" Matrix moment and successfully block a few attacks in a row.
Crusader Kings 3. You know those map-painting Grand Strategy games, where the goal is to conquer other territories? One of those, but you're running a noble dynasty whose fortunes rise and fall, even passing between the overlordship of different countries and kingdoms. A lot of personality. I guess it's not as innovative as it once was, since it's spawned imitators at this point. Hm.
Ring of Pain. It's... hard to describe.
Phasmophobia. Multiplayer only. You hunt ghosts. Not like, 'combat' hunt ghosts, like 'You need to find evidence of ghosts' hunt ghosts. But the ghosts definitely hunt you back - in a much more malicious way.
Death Stranding. Walking simulator. No, not like 'You don't do anything but hold down the walk button', like 'You need to keep your balance while carrying things' walking simulator. Immensely weird.
Star Trek: Bridge Crew. Multiplayer only (at least practically speaking). Each person plays a separate member of the titular bridge crew, and cooperation to achieve even simple tasks is key.
Gods Will Be Watching. A series of puzzle scenarios about calculated risk, failure, and learning the rules anew each time.
- I strongly object to the characterization of Death Stranding as a walking simulator. Walking place to place is core to the experience for maybe one quarter of the game. Once you get to the largest area and continue unlocking new tools and features, you spend very little time walking. It also dismisses combat, which I felt was considerably more prevalent than I expected.
  Cool picks though.
  
  I feel like I spent a good portion of my time walking and finding ways across rough terrain even after all the fancy gear was unlocked. The motorcycle could get you maybe half the way, usually.
  I mean, at least until the zip-lines. Those ruined the game. Honestly, the rebuildable roads were a bad inclusion as well. Sitting on top of a hill, looking down at the streams and terrain around you, figuring out the best route with your tools, was peak satisfaction in that game.
- +1 for Majesty. The combination of fawning over your champions while also absolutely cursing those stupid useless fuckers was fun.
- Majesty (Majesty 2 is okay, but lacks the charm of the original, but YMMV) - you run a kingdom full of heroes. The catch? You don’t command the heroes. They have their own AI and goals and you have to offer incentives and place the necessary buildings appropriately to both enable and encourage them to do their jobs of saving the kingdom.
  I loved that you could build temples and get specialty priests for 5 different gods, but never more than two in one level, because some of the gods were opposed to others, including the one I never used because they were monotheists and I didn't want to give up all other types of priests.
  Also that every hero type had their own priorities and preferences and would do what they preferred barring a significant bounty on something else. Also that Rogues could fuck you over if a hero died and you wanted to use the resurrection spell on them because a rogue near where they died might just rob their grave.
  Star Trek: Bridge Crew. Multiplayer only (at least practically speaking). Each person plays a separate member of the titular bridge crew, and cooperation to achieve even simple tasks is key.
  Artemis Spaceship Bridge Simulator did it before that, in 2010. ST: Bridge Crew is more or less "Artemis but with Star Trek branding". Artemis just released a remake/sequel-sort-of-thing a bit over a month ago (called Artemis Cosmos, though it's had a...rocky...launch so far) that's a complete rewrite from the ground up.
  And when I say they did it first, I mean to the point that some of the reviews describe Artemis by likening it to being a member of the bridge crew on the Enterprise, because there wasn't a game like that on the market.
  Gods Will Be Watching. A series of puzzle scenarios about calculated risk, failure, and learning the rules anew each time.
  Under known, under appreciated but fantastic.

Tunic is incredibly unique and I can't say I've played anything like it. On the surface it's a classic dungeon crawler zelda inspired thing, but once you play.... Really any amount of it, you start to see past the veil and the real game is revealed to you. Even after completing the entire game and all achievements, there is technically more of the game available to be explored.
Outer Wilds (not to be confused with Obsidian's Outer Worlds) will be an absolute bliss for anyone who enjoyed portal or superliminal. It may be the single greatest puzzle/exploration game ever made, with no exaggeration.
Return of the Obra Dinn was a game that I could not put down. I played it in one sitting beginning to end. I was enthralled and I felt like Sherlock fucking Holmes. It is a very unassuming game but by God, you will be gripped. It stands up there with Outer Wilds as being a game that absolutely propelled itsself up to one of the best of its genre (this one being Mystery/Puzzle)
- Bump for Outer Wilds. Genuinely an amazing and unique game. I've never seen another "found knowledge" game mechanic like this.
- @Spood_Beest@lemm.ee @frank@sopuli.xyz
  If you haven't played either of the other two games I mentioned, I think you'll thoroughly enjoy them. All 3 of the games are absolute masterclasses in how to hand the player knowledge that transforms their experience of the game, over and over again.
  
  I've heard great things of outer wilds, just wishlisted it. I hadn't heard of Obra Dinner but it's Lucase Pope! The Papers, Please creator. Instant buy from me.
  Thanks for the suggestions, my SO and I are stoked to delve into more mystery and confusion
- I so wholeheartedly agree with Tunic. It absolutely blew my mind to complete. I'd love to experience that again.

Fez: a 2D plateformer in which you can change the perspective to create ways to unreachable plateforms
Baba Is You: a puzzle game in which you move blocks with words written on them, combining them to create small phrases which become new rules of the game.
- BABA IS WIN
- Super Paper Mario for the Wii also has a mechanic like that. You're in a 2D paper world (obviously) but you have the ability to temporarily turn 90°; walking through enemies and opening the possibility to i.e. pass some walls.

Impossible Creatures - an RTS where you slurp up DNA from local wildlife and use that to create weird hybrids of multiple animals, then produce those as units that you control to complete missions. Great concept but I think it ended up being a bit unbalanced.
Papers Please - pretty unique gameplay in that you had to literally read through paperwork and approve/reject people at a border crossing. Good social commentary.
- Gosh Impossible Creatures was the coolest game as a kid. I wish we'd get a remaster.

Katamari Damacy - The objective is to roll a ball-like thing called a katamari, to roll up objects, and make the katamari bigger and bigger. You can roll up anything from paper clips and snacks in the house, to telephone poles and buildings in the town, to even living creatures such as people and animals. Once the katamari is complete, it will turn into a star that colors the night sky. Sounds weird, but it's super fun, trust me. Plus, it's soundtrack is kickass.
- Great soundtrack too

- Also, there's a Steam achievement you get by not playing it for 10 years.
  Wasn't that 4 or 5 years?

Tunic and Outer Wilds
Both have a heavy focus on using knowledge as your core resource in the game, and obtaining new knowledge as a primary gameplay loop.
- I can't believe I typed out a whole recommendation about tunic and outer Wilds, and then scrolled down and saw your exact same recommendations. Lol. I guess excellent games are universal
- I had a moment in Tunic where I realized what the references in the manual to the [HOLY CROSS] were talking about, but I don't think my revelation was the typical.
  I'd actually figured out the [HOLY CROSS] really early on, solved a bunch of puzzles using it, got some manual pages I probably wasn't supposed to have yet, but didn't know that the thing I was using was the [HOLY CROSS] because I lacked the context of a certain page that spells it out and based on some comments and videos elsewhere is the point where a lot of people first figure out how to use it.
  It probably didn't hurt that I was fresh off The Witness and my brain was subconsciously looking for tricks of perspective and environmental puzzles, which Tunic is absolutely full of.
- I feel like Tunic leans too much on the LttP format to be called unique but it is a delight
  
  Ah yes, LttP... Obviously, I know what this means, but for others who don't maybe you could elaborate?

Maybe Antichamber? It‘s a first-person puzzle game like Portal, but based on the idea of the „rooms“ changing as you go through them, so each room basically has its own mechanic to figure out
- It's Portal on acid, a great game. Also Manifold Garden by the same guy.

Factorio - its a logistics rts but the pollution mechanic is different. Instead of just gather resources to build things which build bigger things, you also make pollution as a side effect. This feeds the native monsters and also evolves them. Managing your pollution cloud is a strategy. That or build massive defensives for when they come to eat you.

Faster than light - manage crew in a 2D strategy environment and jump around in space. Pretty unique gameplay which only recently got some clones.
Teardown - Work as criminal stealing stuff, but the clue is you can destroy everything and you need to create smart parkour to steal stuff right in time before the cops arrive. Also you can sandbox play it if you get bored.
Terra Nil - Bring back nature to a destroyed earth, with relaxing and calm mechanics. Highly recommend.
Others: FEZ, solve puzzles. Deep Rock Galactic, because dwarfs being this much dwarf is just dwarftastic. Rock and Stone!

Death Stranding
I've never played such a unique big budget game. The core mechanic is terrain traversal to make deliveries, and the game continues to give you tools throughout it to accomplish that.
- The BT's were scary enough that I couldn't keep playing, I got to a bit after the part where you get the exo legs.

In Return of the Obra Dinn you play an insurance claims investigator. You can magically view the moment of somebody's death and hear the audio prior to it to aid in your investigation of a ghost ship.

Return of the Obra Dinn.
- Was gone be one of my suggestions. This game is powerful good. It is a true mystery with you in the drivers seat in a way no other game can touch.

Wow. I'm super impressed with all the suggestions here. I'll add a few of my own that haven't been mentioned yet.
Her Story - you query a police archive database for video clips, eventually revealing the plot. Kind of a mash between a murder mystery book with the pages out of order and Google. If you like it, check out Immortality
What Remains of Edith Finch - all you can do is walk around a very unusual house. The narrative reveals itself as you do so. That narrative is fantastical and heartbreaking and also very sweet.
Crawl - multiplayer game - you are all trying to escape a monster and trap filled dungeon. One of you is alive and the rest are spirits who can possess the monsters and traps. Any time a spirit kills the living player, they become the living player. Unique boss fight at the end where multiple spirits control parts of a huge boss monster.
- Some of the CW Warnings for What Remains of Edith Finch (spoilers obviously): ::: spoiler spoiler Drowning, child death, divorce / arguing, pregnancy, child birth complications / death :::
  
  Thanks for that! I actually had to put the game down for several months because my child had just been born and I couldn't handle one of the scenes in the game. It was heavily telegraphed, so I had time to stop the game before anything upsetting happened. And when I went back to it months later it wasn't nearly as bad as I thought it might be. But yeah, it's a game about the death of many family members, told through metaphor and fanatical imagery.

- Also the story is one of the best in the entire history of gaming (IMO).
  The other of course being To the Moon.

I remember ‘Braid’ being very good. A number of different time manipulation mechanics throughout the different levels of the game. Puzzle platformer.
There’s an anniversary edition planned so maybe stick it on a wish list for now.
- About that anniversary edition, is there any information? Since the tralier release, it's radio silent.
  
  I don’t know, sorry. Just saw that detail on the wiki page but didn’t want to link a page of spoilers.

Cultist Simulator is pretty unique... not necessarily in a good way. It's a storytelling/puzzle game with some great writing if you can power your way through the gameplay. The mechanics are deliberately very obtuse, with no tutorial, to emulate the fact that diving into the occult is confusing and dangerous. The end result is that the game is very unique and cool, but it's absolutely not for everyone. TL;DR on the basic mechanics: you have a handful of verb boxes, such as Talk or Research, as well as various cards that you can slot into them. Each card has a variety of tags on it. Depending on which cards with which tags you put into the various verb boxes, you get different results.
- Cultist Simulator somehow made me feel the same fanaticism as I assume a cultist would feel. It can be very addicting, chasing the endgame, driven by curiosity and desire for power. Not for everyone though.

Outer Wilds is amazing and the mechanic is unique.

Heaven's Vault
You play a space archaeologist, and the big central mechanic of the game is translating things written in the Ancient language.
Ancient is written using ideographs, and more complex ideas are represented by combining glyphs that describe the concept, like ever more complex compound words. There are art of speech markers, glyphs that describe how other glyphs in a word relate to each other, intensifiers, and even a few cases where super common words are just the combination of other basic glyphs into a single composite like a Norse bindrune (for example the symbols for creature and knowledge overlap to make person, an intelligent creature). 46 base ideographs, but that includes digits, so it's only 10 more than English.
So for example, a word that reads NOUN-person-Sub/Obj CONNECTOR-NOUN-knowledge-person means "Emperor", because noun-knowledge-person means "law" and thus the result is a person who the law belongs to, aka a ruler or in the context of an empire the emperor. Replace that noun marker glyph at the beginning with the adjective marker glyph and you would have "imperial", the quality of being emperor-like.
One of the longest words to appear in the game translates as "mouse" and it's 21 letters long and is literally something like creature-CONNECTOR-many-many-Sub/Obj CONNECTOR-ADJECTIVE-NOT-ADJECTIVE-CONNECTOR-many-creature-CONNECTOR-ADJECTIVE-ABSTRACT NOUN-person-CONNECTOR-light-NOUN-plant-CONNECTOR-rock, which is several words stitched into a compound word, where some of those words are themselves compound words (the idea is something like "creature like a very small pig", but the word I'm calling "pig" means "creature that is happy in the soil" where happy is something like "the quality of a person who is metaphorically full of light" and "soil" is "plant-earth"). Those CONNECTORS are letters that are used to build compound words.

Exapunks is a programming puzzle game set in a retrofuturistic cyberpunk world with early '90s aesthetic. The tutorial is in a form of an in-world zine. For me it was very immersive.

Qube and anti-chamber if you're a fan of superluminal

Getting Over It - the controls themselves are your enemy. A different take on the same concept: Octodad / Manual Samuel.

Prison Architect is pretty cool and unique.
Portal reloaded adds time portals ontop of the normal portals.
Splitgate is an FPS that adds portals on top of Halo style combat. Very fun but may be hard to find a game these days its kinda dead.
Age of empires 3 is an RTS that adds shipments. These shipments increase the pace of the early game and allow for way more personalized play as well as allowing players to react to different things without shifting their entire build order.
GTFO is a horror fps where you and 3 other human players take on raids and these raids are changed each season. When the raids are retired they are gone. You must beat the lvl 1 raids to unlock lvl 2 and so on.
Radio Commander. Its an RTS where you sit in a tent in Vietnam and give and recieve orders via radio. You have a map that you can mark where things are based on the info you get.
- I hadn't heard of a few of these and they sound really enjoyable. Thanks for sharing!

I really love Terra Nil.
You basically have to restore a wasteland back to lush, green nature.
Much like a city builder, this is achieved by putting down buildings. The twist is that at the end, you can't leave a trace so you need to demolish everything again.
It's not a long game, but I thought it was very satisfying. A relaxing puzzle/city builder with soothing music.

Neon White: A parkour FPS puzzle game where you cards are your weapons
Rollerdrome: Best way I've heard is described is: Doom x Tony Hawk

Graphwar is definitely unique. It's a bit like worms, but you fire mathematical functions.

Before Your Eyes
The recently deceased Benjamin Brynn is on his way to the afterlife. The player must interact with Brynn's memories through an eye-tracking webcam to progress, as the game reads and responds to the player's eye movement and blinking - from Wikipedia
It tries to emulate life flashing by your eyes as you are dying. I haven't gotten around to play it but, the concept is cool nonetheless.
Found about it from this video - https://www.youtube.com/watch?v=LTI1WCopTsg
- When I saw this thread I thought of the exact same game, which I heard about in the exact same video

Do Not Feed The Monkeys - spy on people via hidden cameras for fun and profit. It's mostly point and click but it's fun.
- In a similar vein, Not For Broadcast. Pick what camera feed to show, what to censor, etc. Will admit I haven’t played it myself and am going off the Steam description page, but it seems pretty unique mechanics-wise.
  
  I have this game and it looks to be amazing, but OMG I can't keep up with the pace of dealing with the cameras and censoring stuff. I want to love it but I'm just not quick enough.
  It definitely fits the criteria that op wanted tho, good call

I have a couple kinda unique things to suggest. There is a small indie game called Eversion that you can find on Steam. The core mechanic is about shifting to these different planes of existence to finish levels. You can only shift at certain places and shifting opens up pathways that weren't there before. Its retro style graphics and otherwise very simple controls. The Turing Test is a puzzle game like Portal, but instead of portals, you have a gun that can be used to move energy orbs from around the rooms to unlock doors. The game feels like it encourages creative problem solving a lot more than most puzzle games. Catherine. Catherine is a game in a few styles. You spend part of the time at a diner/bar interacting with people. Then you go to sleep and in the dream world you ascend towers using moveable blocks that you must climb. Sometimes you are chased up the tower by a boss enemy. There is no combat in the game. It's about ascending the tower as fast as possible at night and progressing the story by day.
- The Turing Test is a puzzle game like Portal, but instead of portals, you have a gun that can be used to move energy orbs from around the rooms to unlock doors. The game feels like it encourages creative problem solving a lot more than most puzzle games.
  Along those lines I'd want to recommend the Talos Principle as well.
  And also the Witness, which does fantastic things with environmental puzzles.
  
  The Talos Principle is fantastic. Probably my favorite puzzle game. The sequel is finally happening as well.

Donut county, you're a hole in the ground growing as you consume the environment.
Katamari damacy, you're a ball rolling over and collecting items in the environment and steering is like steering a canoe.
Octodad, be an octopus in a suit pretending to be human who can't control his limbs properly. I am bread is similar.

Crypt of the Necrodancer: Roguelike to the beat! Dance pad compatible.

Patrick's Parabox: Push blocks around to activate switches and reach the exit but the blocks can be pushed into and out of each other recursively, it's awesome
Fez: Already been suggested so +1 for this, lovely game

Poppy Playtime (2021) : controls the extendable arms separately and solve puzzles that way
Older games:
Psychonauts (2005) : some of the scenes toy around with gravity
Half-life 2 (2004): the gravity-gun was groundbreaking.
Serious Sam (2001) : just a shooter, but the quantity of enemies is so huge that you need to figure out different strategies. It's sort of like geometry wars only in first person view and with gory graphics.
Glover (1998) : it's a 3d platformer, where you control a glove, which needs to get ball through the level.
Head over heels (1987) : control the 2 characters Head or Heels separately or together to solve puzzles.( It was recently released on steam. I haven't tried the remake, but the original can also be found on emulators or online)
- I was going to say that Serious Sam isn't terribly unique. But you're right about the scale of the battles being far larger than anything else like it. Good call.

Snake Pass - "What does a platformer look like without jump (or a regular walk for that matter)?" It's really fun and unique.

The Witness
- This was what I was going to add. It's basically just walking around and finding panels that have small 2d mazes on them, and solving the mazes. Sounds simple and honestly quite boring, but it quickly becomes far more special and ends up being so good.
  Some of the solutions made me feel like my brain was folding in on itself before clicking into place

Kenshi, or noita are the 2 indie games I can think of
Kenshi is unique in a way that it doesn't give you main character vibes. You're a nobody like mostly everyone else.
- +1 to kenshi. I have ~1500 hours in it. Noita is dope too, but Ive barely touched it as I suck at it
  
  I beat the tutorial boss, but I have yet to defeat the high alchemist

The game is definitely not for everyone, but ProsperousUniverse kind of stands alone when it comes to people’s descriptions of niches/genres.
The game is an economy/real-time MMO with no real PvP. “Real-time” not like an RTS but as in “this operation takes many hours or days” and everyone has that same time burden.
It’s a game where planning far outperforms “always online” gameplay, so people end up learning spreadsheet software to optimize everything for themselves.
In addition, the UI is modular like a Bloomberg terminal, so it feels right—you feel like a trader.

Against the Storm Rogue lite city survival builder with gorgeous art, awesome game mechanics and a fantastic dev team whom have basically built the game in collaboration with the community that’s risen around the game.

Persona - a turn based Pokémon-like RPG fused with a social simulator. Your main way of getting stronger isn't by simply levelling up (although it helps) but by fusing multiple monsters that you catch and spending your limited time available with comrades.

Its retro and really rough around the edges (and QTE heavy) and is more of a life sim than a traditional adventure game, but Shenmue I & II introduced day/night cycles with NPC schedules, has a fun martial arts combat system, and the story is kind of like an 80s martial arts film with a detective kick. There's also gambling, drinking, a little bit of working at the docks, darts, retro arcade games, and some sleuthing to progress the story. Your progress from Shenmue I carries over to II
But again its rough around the edges and sometimes referred to as QTE simulator (or Dock Worker Simulator, as I jokingly call it). But somehow, all these elements blend together well to create a unique game. Not going to be for everyone but I really enjoyed it
Final note: I highly recommend using a controller. I ran into issues with KB+M, especially after remapping keys. It broke some of the QTEs.

I am not sure if it qualifies but Paradise Killer is pretty unique all-around. It may seem walking-simulator-ish but the presentation and the overall game-design are definitely a stand out. You're trying to solve a murder mystery and it's completely up to you as the player to decide when you've gathered enough information to make a conviction. There is practically no hand-holding either which is quite rare for a mystery solving/detective game. I know it might not exactly be what OP asked for but I think the game is worth being recommended more.
- There is really something very different about this game. If you point to any individual part of it, there are other games that do that thing. But all together, it's quite unique. And it's a pretty fun game.

The World Ends With You (DS): Asymmetric action RPG where your left hand and right hand are playing different games in parallel, which is deeply connected to the game's themes of individual experience and semiotics. The switch remake unfortunately ditches the core gameplay to make it more widely accessible but the original game is worth getting into.

Duskers - scifi, space ships but with a bit different pov then one would expect
Prosperous Universe - someone already described it here so vouching for it too
- I come back to play Duskers often and I always enjoy it. There's not much else like it.

Battlezone '98: One of the first notable RTS/FPS hybrids. You drive hovertanks and you build bases and you command other tanks. Set in a secret live war on the Moon, Mars, and Venus between the USSR and the USA during the cold war.
- I don't see a unique core mechanic in that, there are lots of RTS / FPS hybrids, both single and multiplayer.

I don't know how many other games have done this (or if anyone actually cares), but Me And My Shadow. It's a 2D puzzle platformer where you have to record your movements to move the shadow version of you in order to reach the end of each level.
It's a discontinued open source game that can be found on SourceForge and has a couple different level packs available for when you complete the ones already included.

Opus Magnum. It's an optimization puzzle game. You have to assemble mechanical arms and other bits (that grab, swing, rotate, push, and pull) into contraptions that assemble resources that look like molecular diagrams. Optimization puzzles aren't unique but I felt like the pieces you build the contraptions out of in this game are pretty unique, the game is on a hex grid so rotation can play a big roll. Another interesting thing the game does is that to beat a level you simply have to accomplish a proper assembly, which in itself isn't that hard, but the game grades you on three different metrics (speed, size, cost) and gives you no overall score to tell you how much you should value each metric. In this way it is up to your preferences what you want to optimize for if anything. I had fun trying to minmax every stat separately on every level before building my "compromise" machine was not supposed to make big sacrifices in any field.
A lot of people have mentioned it but I definitely recommend Obra Dinn, haven't played a mystery game as unique and enthralling.

Dwarf Fortress mostly doesn't have unique gameplay mechanics or anything; but the Legends viewer certainly is a unique feature, due to how all the systems work together to weave randomly generated stories and history of the world through the entire world generation process. So even though you didn't play the game through all those years, the game still kept track of everything going on while simulating the world creation and you can go through it and see all the battles, conflicts, migrations, rise and fall of civilizations, deaths of monsters, etc.

Very surprised that A blind legend didn't make it here, among all those suggestions.

Death Stranding makes the player think about how to walk over difficult terrain with a large amount of cargo on their back without losing their balance and falling down. Most games allow you to run as far and recklessly as you want without having to worry about falling, so it was interesting to actually have to work at it, at least before you unlock various modes of transportation.

The first two games that came to mind are unfortunately only available on PS4. I'll mention them anyway, just in case they come to PC in future or someone else that has a PS4 is interested: Tearaway Unfolded is a really sweet game in a paper craft world. You manipulate paper scenery to help with platforming and really customise your character in creative ways. Just a unique and charming game. And Gravity Rush 1&2. These games let you alter gravity to fly around a beautiful open world - I've never played something with a traversal and combat system like this.
I agree with Obra Dinn and the Witness as mentioned by others!
This is probably a weird suggestion, but you could emulate Metal Gear Ac!d 2 (PSP game). It's a stealth game (like the rest of the MGS series) mixed with a deck builder, so your actions are dictated by the cards that you play. The second one in particular perfects the formula IMO. It's super satisfying and I'd love to see more games of this type!

Soul Reaver comes to my mind. Old game but i think it‘s still holds up.

Ancient Art of War. Really old RTS where food, morale and exhaustion are all-important. You'd think it'd be a micro-management nightmare but it plays smoothly. Unfortunately not multiplayer and never remade or even imitated, for some reason.

The Misadventures of P.B. Winterbottom