This question was raised on the latest Chicken Chess Club podcast by a listener writing in who wanted help trying to play blindfold and who said:
What do you see when you try to visualise the board? Do you see a 2-D board as on the screen? Do you see a 3-D board with pieces as they would be in real life? Or is the whole thing somewhat more abstract?
The question appears just before the hour mark. The three main members of the Chicken Chess Club are Laurent Fressinet, Peter Heine Nielsen and Jan Gustafsson, all 2600+ GMs. Here is a rough, much abbreviated transcript of what they said.
Laurent Fressinet: I don't see a board. I see an area of power. When you play 'e4' you don't see the rook on 'a8'. We didn't learn to play blindfold. It came just naturally when we were kids. We talked about games and said some moves. We didn't think about it. We just did it.
Jan Gustafsson: Same for me. The pieces aren't 2D or 3D. They don't have colour or shape.
Peter Heine Nielsen: For me clearly 2D but I don't really see it. It feels like a computer screen. You don't see it. Larsen said "The board you see in the mind is the most beautiful. You don't see it. There is no distraction." Any kind of chess set annoys me because it distracts from the board in my head. When someone says "These are beautiful pieces", no, the beautiful pieces I have are the ones I have in my head which are just completely clean and it only matters about chess
Jan Gustafsson: No, and the amount of detail you need and we don't need colour or shape or anything on top of the knight. You just know that's a knight and that goes there.
Peter Heine Nielsen: And, no, we've not trained it one bit. It's a necessary skill. If you read a chess book then you have to be able to see the position. When I was in my late 20's I was playing in a tournament with Peter Svidler in Denmark and they were giving printouts of games from Dortmund. Kramnik beat Anand in a Qc2 Nimzo. At some point Svidler laughed and I said, "You're laughing at the opening" and he said, "No, bishop exchange on move 32." That is way too difficult for me. I can't take a piece of paper and play through the game like that. (Thanks to Allure for the link the game Svidler comments on is here)
The full segment is 7 or 8 minutes long so it is worth trying to listen to the full segment. There is a lot of amusing stuff - JG's take down of Svidler's childhood, PHN's humble brag about giving a blindfold simul in which he beat Magnus Carlsen (albeit a very young Carlsen). For those with a philosophy background PHN's discussion of the board in the mind has echos of Plato's theory of forms.