Update 26th April 2024: As has been pointed out to me overnight by a thousand helpful, furious strangers, describing a Sega fangame (one with Saturn button prompts, no less) as "SNES-style" is a crime deserving of imprisonment in the deepest depths of the Labyrinth Zone. Speaking as a former Genesis/Mega Drive diehard, I can only hang my head.
It's essentially a sequel with very different mechanics. Also there's a proper singleplayer campaign with bots, different cups and achievements. It's a bit difficult but I'm having fun with it.
The onboarding is... Pretty rough though. The tutorial is actually half an hour long.
My understanding is that they reconciled both names some time ago, the character's in-universe real name is Dr. Ivo Robotnik and Eggman is the moniker he's known for.
I see Robotnik as an entirely separate character to Eggman. The AOSTH/Mean Bean Machine character was a bumbling idiot, and Robotnik Prime from SATAM/Archie Comics was a brutal overlord.
The Sonic fandom continues to amaze me. For every mountain of lewd fan art and crappy original characters created by fans, you get an incredible fangame that absolutely trumps official efforts from Sega themselves.
Pulling off a kart racer in the Legacy DOOM engine of all things is a seriously impressive feat.
I like the fact that Eggman is not the villain in this. I'd like to see more of this in future Sonic games. We've seen plenty of times where other videogame mascots have teamed up with their arch rivals to stop a greater threat.