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Why it works
2...f6? already weakens the e8–h5 diagonal, but the game is only truly lost after 3...fxe5?? — recapturing the 'hanging' knight opens the f-file and invites 4.Qh5+. From there it is a textbook king hunt: 4...Ke7 5.Qxe5+ Kf7 6.Bc4+ drags the king forward, 6...Kg6 7.Qf5+ Kh6 8.d4+! opens the c1-bishop with tempo, and after 8...g5 9.h4! the pawns finish what the pieces started: 11.Qf7#. The knight on e5 was never free — it was the cork on a flood.
Refutation
3...Qe7! is the only respectable move: it attacks the e5-knight without opening the f-file, and after 4.Nf3 Qxe4+ Black regains the pawn, staying 'only' clearly worse (engine −1.6) thanks to the hole f6 left behind. The rule of the Damiano: the knight on e5 must be pushed, never taken.