It doesn't take long to go through all of the permutations in your head and figure out that it's something really odd, but this line in the second paragraph should have let every reader know that the solution was gimmicky: "If I told you that the solution is a VERY unusual move that is no longer strictly within the bounds of the rules of the game then that might help you a little bit." From then on, I read the story instead of trying to solve the problem.

He said at the very beginning of the article that it is no longer a legal move. I don't know why you are surprised to find out that the move isn't legal now. But it has nothing to do with "flipping over the board". It's a perfectly reasonable seeming move.