On the other hand, recovering the full board state in a single forward pass? That takes some special training.

Same goes for meatbag chess. A correspondence chess aficionado might be able to take a glance at a list of moves and see the entire game unfold in his mind's eye. A casual player who only knows how to play chess at 600 ELO on a board that's in front of him would have to retrace every move carefully, and might make errors while at it.