The key move allows the B to be captured in seven different ways, each leading to a different mating response.
The penny dropped when I saw the a7 P seeming in a position to promote and mate, if the black Q could be decoyed away from the a-file - but what would induce the Q to vacate the file? There is no reason for it to take the B in the set position, so the key move must involve movement of that B.

You are correct; I did not even notice that capture was possible by the king,