This is clever but it can't be a good captcha. Computers are really good at understanding a visual chessboard and even better at actually finding the best move.
I had the same thought, but on further reflection, while it's very doable to get a computer to figure it out, it still seems like quite a bit of work to have it read, parse, analyse and play the move for this specific page, on this one website for a low value payout. Additionally there is natural language question that has to be understood for what you are supposed to do - it doesn't necessarily have to be mate.
Since security is fundamentally increasing costs enough to outweigh the prize, I feel like this makes it.