It tripped me up at first, too, but @mrmisses@lemmy.world is correct. Here’s the breakdown:

Stalin: Is it necessary?
Girl: No.
Stalin must now remove things from the board that are necessary in his opinion.
Stalin: *removes food* (which implies it’s necessary)

If the girl said “Yes”, then Stalin would have to remove the things from the board that aren’t necessary in his opinion, for instance, food.