I suppose you could run it on the cloud yes. Simplified it just has a database that it draws from and generates new material from it, that is why there is some controversy regarding AI and art and how that affects copyright if the AI is trained on copyrighted material.

So, lets take a game like pathfinder. If you were to take chatGPT, and instead of the database you trained it on being a snapshot of the web ~2 years ago, you give it the entire history of the world, you could have it generate new content pretty easily.

There would be issues in making sure it is internally consistent, but yea I suppose it would be possible using a cloud based solution.