Consider: There are probably sets from TV shows that you have seen many times. Would you be able to navigate them in the dark?
Visualisation without a chess set
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When you live somewhere for long enough, you can usually wake up at night, and go to the bathroom in the dark, without bumping into the furniture, because you "know" where everything is.
This has nothing to do with becoming a GM or a president.
This likely is more a result of muscle memory than visual memory. Basketball players can sometimes make spectacular shots while being knocked down, even if they can't see the basket, because they have practiced throwing the ball into the basket so many times that they "know" just where the basket is by seeing just where they are on the court. But I doubt that if Steph Curry were blindfolded taken to a basketball court and told "you are 32 feet from the basket and 12 feet left of center court" that he would have much success.