They didn't try to encode all legal positions though, only ones that were actually reached in their database of games. It sounds very plausible to me that this allows a lot of simplifying assumptions that cut the state space by about 60 bits
I can put it all in, say, 24 bits, if my database is small. 140k games, 120 positions each. log(140000*120)/log(2) ~~ 24.001, and surely there will be some duplication.
The encoding is just the index number of the game + move that resulted in that position.
