It took me a while to recognize the actual mating pattern here- that pawn on c5 plays an actual role in probably the most critical line.

1.g5! Nh5 2.Re8+ Kg7 3.Rd8!

White is opening e8 for the knight or the other rook- the fork from f4 is irrelevant now:

3.....Nxf4+ 4.Kf3 Nxe2? 5.Ne8+ Kf8 6.Nf6+ Ke7 7.Re8#

So, at move 3, black has to open up a hole for his king with

3.....h6 4.Kf3 but now black can't deal with the twin threats of Ne8 or Ree8, and must lose at the very least, the exchange.