Given the current upper bound on legal chess positions is 7.7e45 ≈ 152.4 bits, you either have found a better upper bound or your memory doesn't serve.
Now I'm wondering if it is a "legal" chess position to get the pieces to swap sides ... a solver to find how to do it would be amusing.
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