It's not entirely clear how LLMs that can play chess do so, but it is clearly very different from the way other machines do so. The construct a board, they can estimate a players skill and adjust accordingly, and unlike other machines and similarly to humans, they are sensitive to how a certain position came to be when predicting the next move.
Regardless, there's plenty of reasoning in chess.
It’s very clear how, chess moves and positions are vector encoded into their training data, when they are prompted with a certain board state, they respond with the most probable response to that. There is no reason.