I've been doing almost exactly this with Mafia (aka werewolf): running games where LLMs play against each other, with humans able to share the lobby. It's been a hit on family game night so far, because it allows our group to "fill out the cast" with a lot more characters than just the human players and add a lot of variety without needing a huge group.

My experience is that text-first, turn-based games are a particularly natural interface for LLMs vs graphical games (though you can provide a harness of course). They read a transcript, maintain a theory about what the other players know, then speak or choose a structured action. The important architectural problem is to represent the game state and actions in a way they can do successfully, particularly for cheaper models. But with a few human players + a frontier model or two + a backfill of cheap extras to provide chaos, it is super fun.

My favorite failure so far was a Kimi player getting fact-checked by the group, switching into third person, and concluding that the case against itself was compelling. So it voted for itself to be eliminated.

I collected a few examples here: https://botmafia.games/#emergent. No public instance yet, as I'm having fun iterating ideas on game nights, but it provides some flavor of what kinds of fun I've been having.