[SilasX]

I see several levels of compression:

1) First, as you mentioned, the limited symbol table for expressing all the moves.

2) But not every move is possible; you just need a way to order all the possible moves and then say the nth of those moves.

3) Even better: not all of those moves are equally likely. You can define (n cycles of) a chess playing engine that ranks all moves and reserves shorter symbols for the best moves (as judged within that time frame). Players tend to select higher ranked moves, so that’s another regularity to exploit.

Of course, 3) comes at the cost of compression/extraction time.