Welcome to the forum.
Without going into game development in general (which is outside the scope of this forum), to utilize large language model technology in a game, a popular approach is to create detailed personas for individual agents and allow them to freely interact in a game world.
One poster recently showed such a game here: I've built a prototype for a detective game
There are numerous research articles on the topic, a review article (that contains references to related work) is at [2304.13269] Games for Artificial Intelligence Research: A Review and Perspectives
Hope this helps!