Ask Lemmy

If you want to scratch that "players have their own genre" itch, you might look for asymmetric gameplay. There are a few video games, Death by Daylight being the most famous, but many in the "monster vs party genre". There's a shark one I can't remember the name of, and a few eothers. There's also Davigo, a VR game where the VR person plays a giant floating head that tries to smack a little person running around, played by your friend on a regular PC in FPS mode.

Sort of tangent to those game, of course there's your hero shooters and MOBAs, which are much more aligned objective wise but with very different gameplay per hero. I'm a sucker for DOTA which has very different heroes, and then there's your Team Fortress or Overwatch style FPSes too.

You've also got really expansive games where you have access to all the gameplay loops but people can pick what they want. Think like a multiplayer Stardew Valley. Elite Dangerous comes to mind as a game where you can go do space dogfighting, space trucking, exploration, or mining - and they all play pretty differently. You can even combo, like mine dangerous areas with a fighter escort to protect from pirates who want to fight.

Really outside video games, but closest to what you're talking about you might like the board game Root. It is a board game (though there's a PC version), but it plays VERY differently depending on which forest creature you are. Cats play a traditional conquer and control (think Risk), the Birds play an action chaining card game (think like a deck builder), the Racoon does his own like exploration game, etc. but they all interact in different ways when their goals come at odds with another. It's an awesome, super creative game. Big fan.