chess online

White's Rb1 move is required here. If 1 . . . h2

2. Rb1 Nd3
3. Rh1

then the pawn doesn't promote and white even saves its rook. It isn't reasonable for black to expect two moves to queen.

That still violates the tactics insistance on least possible moves since it is 3 moves instead of 2. So the computer should have expected the tactic you noted in your solution above because white has a way to extend the play.