To repeat: the idea for a mate is there because Black’s f-pawn is missing. White therefore plays with ways to put pressure down the diagonal to g8 and then mate with vertical pressure against h8. Again he only has one heavy piece and so won’t be able to execute Greco’s mate in traditional form, but if White were able to get his knight safely to g6 he could mate with his bishop from d5. At present the g6 square is guarded by the pawn on h7 and d5 is guarded by Black’s knight, but now White sees a way his queen can be useful: he plays Qxh7+, almost mating (with support from the f8 knight) except that Black can play NxQ (KxQ is not possible, of course). So White lets him play that, then safely swings his knight into position with Ng6+. Black’s king is forced to g8, and now Bd5# concludes the matter.
Step back from the position and see the ideas in it: spotting the missing f-pawn and the resulting line to g8; moving the knight-and-bishop pair from their current positions onto g6 and d5 respectively; and using a queen sacrifice to loosen both of those squares, and also to get the queen out of the bishop’s way.