You could chat to the AI, and the AI responses can be parsed to trigger in-game actions (e.g. declare war or offer a trade).

Bing, you are playing Civilization as a Nuclear Gandhi.

While I can't prove it wouldn't work, it seems doubtful. How would the LLM be made aware of the game state?

Meta made an AI to play Diplomacy which is able to talk to other players and play the game. It doesn't use a LLM, but it was able to win a tournament against human players.

https://ai.facebook.com/blog/cicero-ai-negotiates-persuades-...