Note that four of the pieces can be rotated 180 degrees, those named X, Z, and I, plus the 2x2 square "O". Including the chess symbols, only piece X is itself invariant under rotations. When any of the other pieces is rotated the board is still checkered properly, but the solution is no longer valid, because black is no longer checkmated and/or the chess position is no longer valid.
If I or O are rotated 180 degrees white is no longer checkmated. If Z is rotated 180 degrees the chess position is no longer valid (pawn on rank 8).