Because those games are just a way to measure how an internal state changes with moves initiated by the ego and initiated by someone else. The point is that there is no consistant internal state because it hallucinates and spotaneously changes. its like telling the language model a story, and getting it to repeat certain facts about it or you make additions to the story. its the exact same thing. It needs quite a lot of "prompt engineering" to push it in the correct direction, and even then its frequently incorrect.