I think this is to some extent true. After I played games of go, I could often reconstruct the moves of the games afterwards, and it was mainly because me and my opponent were generally making high probability (i.e. relatively good) moves. Similarly, you could view words as high probability arrangements of letters, which is the underlying reason we can recognize a word right away and remember its spelling, whereas it is more difficult to remember a random string of letters.
But where this would probably fall apart is if an expert played a total amateur who was making nearly random moves at times. Such a game board wouldn't be encodable into a high probability subset of "words".
So, the question I don't have the answer to is, could a go master recall such a game? I can't say for sure, but my suspicion is "yes", which would weaken the word recognition theory somewhat. So my guess is that they have a few skills working in concert: 1) the ability to recognize and recall high probability patterns, 2) a stronger ability to remember raw go board positions, and 3) they may attach extra significance to a stone's position such as difficulties associated with its placement such as "that stone will break my ladder attack" that make it easier to recall the placement relative to the other stones on the board.