Each of these models has a thinking/reasoning variant and a default non-thinking variant. I would expect the reasoning variants (o3 or “GPT5 Thinking”, Gemini DeepThink, Claude with Extended Thinking, etc) to do better at this. I think there is also some chance that in their reasoning traces they may display something you might see as closer to world modelling. In particular, you might find them explicitly tracking positions of pieces and checking validity.