Is this position a forced win for Black after move 14? In this Lichess game, 

[FEN ""]

1.c4 e5 2.e4 d6 3.Nc3 Be6 4.Nf3 Nc6 5. d4 exd4 6.Nxd4 Nxd4 7.Qxd4 c5 8.Qd3 g6 9. Be2 Bg7 10.O-O Nh6 11.Re1 Ng4 12.Bxg4 Bxg4 13.e5 Bxe5 14.Nd5 Qh4 15. Nc7+ Kd7 16. Nxa8 Qh2+ 17. Kf1 Qh1#


After move 14 White is facing a serious mate threat from the Queen on h4, Bishop on g4, and Bishop on e5. White goes with 15. Nc7+ , forking the King and Rook, but ignoring the mate threat. After the rook capture, Mate in 2 was assured. 

Could white have avoided this mate? By playing, say, Qg3 or h3? Or do both of these positions lead to wins for black, hence, white's strategy with 15 Nc7+ was to prolong mate and perhaps prod black into an unforced error?
The best move would have been 16. Rxe5, which entirely eliminates the mate threat, leaving white with a winning advantage.

r6r/ppNk1p1p/3p2p1/2p1R3/2P3bq/3Q4/PP3PPP/R1B3K1 b - - 0 16


Here, if black takes the white knight (16. ... Kxc7), 17. Bg5 wins the queen as Qh5 is met with Bd8+.