There's actually an interesting section of the book "Moonwalking with Einstein" where it talks about a study was done on chess masters where they showed them the board in positions that would be impossible under the rules and suddenly the master chess players didn't do all that much better than random people.
The suggestion in the book was that really Grandmasters have spent so much time practicing, that they have memorized the game and the board to a certain extant that allows them to more easily handle the board and all the pieces on it cognitively.
Off-topic, but I dislike chess and adore chess960/fischerrandom chess for essentially this reason. It's almost disheartening enough to want a different hobby when you review an online game and realize what you thought was a clever solution to an interesting "puzzle" of a board position was really just one you learned by experience a week ago. More variety in piece arrangement makes playing feel far more like doing chess problem solving than remembering the last time you messed up the same chess problem.
The suggestion in the book was that really Grandmasters have spent so much time practicing, that they have memorized the game and the board to a certain extant that allows them to more easily handle the board and all the pieces on it cognitively.