Very cool. I suspect that much better compression is possible in principle (not that I'd want to implement it) using an openings book or game database and an engine. The idea would be to first record the opening played in the game and the move number at which the game deviates. A lot of work would need to go into figuring out the optimal opening-book size. Then, use a deterministic chess engine with predefined parameters at each move, and record which move number on its suggested list was played (e.g. the top move, second move, third move, etc) with a fallback to manually encode the move if none of the top 8 or so moves are played.

A more sophisticated version would use arithmetic coding, with the predictions of the next move initially coming from an opening book / game database, then coming from the engine. The idea being that most games you want to compress are at a high enough level that the engine gives good predictions ... perhaps one could even tune the engine's parameters for better results. But again, like I said, it doesn't sound like fun to code.

A separate comment: I wonder if the time efficiency issues mentioned are really that severe? Since the problem is so small/finite.