It is after all a Large LANGUAGE Model. There's no real reason to expect it to play chess.

You can get ChatGPT to play a much better game by telling it to display a representation of the current state of the board after each move, that way it doesn't lose track of where the pieces are as easily. But still, given that these LLMs were never specifically trained to play chess in the first place it's amazing how well they do. It'd be like if I set up a chessboard for my dog and 90% of the moves she made were actually valid, rather than simply knocking over all the pieces and then wagging her tail in expectation of the treat she thinks she's earned by doing so.