When people say the phrase "Don't hate the player, hate the game", it removes responsibility from the player
I'm talking in the context of the "capitalist rules". If you say the aforementioned sentence, you remove the responsibility of the player by dismissing the fact that the winner makes the rules.
PS: Doesn't work for every context: if the player aims to change the rules because he doesn't like them, he might see winning as a way to change them. "You either die a hero or live long enough to see yourself become the villain" I guess...
It automatically assumes people are "embedded" in it, and that it is impossible to not participate. It is not as neutral a saying as you seem to think.
You're not as disconnected from the past as you think. The saying has a specific meaning, and it is indeed a forgiveness for those who are embedded in games they do not choose whether the play.
If that's not what you want it to mean, tough luck. The meanings of these things was established before you were born.