I think what you're not getting is that there won't be a "your story". The player will create their own story in cooperation with the LLM. It won't be for every game, but think about games like Skyrim or BotW, where people ignore the main quest and have tons of fun doing whatever the hell they want.

Game devs will still provide structure, "this big baddie is trying to do X, there's this mysterious treasure over here". But the guard rails will be gone, and there will be a real world to explore, not just cutscenes to sit through.