White's pawn chain is constricting Black, forcing him, namely his knight, into passivity on the kingside, while White's pieces have the full run of Black's queenside.

And now, White has two connected passed pawns. All he needs to do is keep Black in passivity on the kingside while he promotes a pawn, relatively unopposed.

Actually, you do want to let him recapture with his knight: 33. gxh4 Nxh4?? 34. Nxe7+

except he wouldn't capture with the knight he'd capture with the bishop to keep the king off g3

Well...to be fair, Black's pieces are still very passive (look at that bishop for instance!) and White still has one passed pawn, and some very active pieces. He needs to watch out for Black's rook for, and make sure he gets his rook behind the passed b-pawn (another principle) before Black does.

Although 40...Bxg5 41.fxg5 ruins White's kingside pawn-structure - the g-pawns are weak and doubled, while the e-pawn is isolated.

Those are all valid comments, and why I was looking at playing g5. But as I wrote, there are other threats from Ng5+ that are about to unfold -- that I didn't see the first couple of times that I looked at the position.

Not necessarily, since 45 ... Rc8 delays the mate, but loses the Knight; leaving you with a 3:1 pawn advantage and an extra bishop. Resignation was in order.

Well played by White.