In the same way mining a bitcoin proves that you've computed a large number of SHA-256 hashes, playing certain sequences of chess moves is attestation that you'

In the same way mining a bitcoin proves that you've computed a large number of SHA-256 hashes, playing certain sequences of chess moves is attestation that you've run a large number of chess calculations—that you've solved a certain large system of constraints that has no real solution other than brute force. Naive cheating (that thing you describe) is obvious, because the cheater is running 6 orders of magnitude more computational power than a human and is proving it to you.