Of course you should not imagine that the knight always is the piece that swoops in to deliver the coup de grace. The knight can be in place on h6 or e7 from the start of the sequence, with work then needed only to open the long diagonal or get a queen or bishop onto it. In this case White has a knight on e7, a strong position because it seals off g8 to Black’s king. And Black’s g-pawn has advanced a square, leaving the long diagonal open; so the only element missing for mate is a bishop or queen there. Now identify the impediment to moving the queen to the diagonal where you want it: the pawn on g6 blocks its path. White therefore plays Rh5, putting a piece en prise to the pawn with a mate threat: Qxh7#. It forces Black to play g6xR, moving his pawn off the sixth rank. Now White mates with Qf6.

While the earlier examples involved the king on g8, you can see that it may not matter if the enemy king is on h8 or g8 or g7 so long as it is confined to those squares and you have them covered—the dark squares by a diagonal piece, and the light square by your knight. (This is a good moment for a reminder that the colors of the squares get reversed if you are playing with the Black pieces, but the logic remains the same: the bishop covers the squares leading to the king’s corner, and the knight covers the square of the other color.)