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.
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.
Regardless, there's plenty of reasoning in chess.