I am sorry, but I thought it was a bold assumption it has an internal model of chess?
EDIT: On re-reading I think I misunderstood you. No, I don't think it's a bold assumption to think it has an internal model of it at all. It may not be a sophisticated model, but it's fairly clear that LLM training builds world models.
We know with reasonable certainty that an LLM fed on enough chess games will eventually develop an internal chess model. The only question is whether GPT4 got that far.
Or, given https://thegradient.pub/othello/, why wouldn't it have an internal model of chess? It probably saw more than enough example games and quite a few chess books during training.