You're correct that the theoretically optimal play is entirely statistical. Cepheus provides an approximate solution for Heads Up Limit, whereas these LLMs are playing full ring (ie 9 players in the same game, not two) and No Limit (ie you can pick whatever raise size you like within certain bounds instead of a fixed raise sizing) but the ideas are the same, just full ring with no limit is a much more complicated game and the LLMs are much worse at it.