So I used the annotation for Lewis Carol's solution on that page and it worked as a private key when I plugged it in blockchain.info, although the address it gave was empty and never used.
Qh5d4Qc4Qc5d5Qf8d6Qc8d7Ne7Nxe7Nf5d8Qe8Qa6Qxe8
I don't know if the fact that it worked as a private key (length of characters?) is a good sign. I don't know enough about private keys...
This is not a private key, I guarantee you that. Private key is just a number, to which is a network version byte added and then double SHA256 hashed + base58 encoded. These series of chess moves you quoted are not a number in any possible representation, and most certainly is not hash because for hash to have such uniform distribution to be meaningful chess game it would be impossible to find private key on which the hash is based. So you are on the wrong path, which doesn't mean there is not something in Alice in Wonderland association with the chess.