There have been attempts, the results were not promising:
https://intfiction.org/t/first-full-game-available-on-new-ll...
https://intfiction.org/t/first-full-game-available-on-new-ll...
The biggest issue is attempts to hack the LLM, to get at hidden gamestate. But I feel this can be easily remedied by just not providing the LLM with hidden game state.
That would keep its behavior passive and restricted to simply the current state, since it would retain no memory of previous actions.