It is a winning position, black will lose for sure.
The only critical move is 1. ... gxh5, because after every other move black simply has lost the knight, while his position is still bad. Therefore it is logical and most interesting to examine first what happens after 1. ... gxh5 which ends in a forced checkmate. Nobody wrote that white will always win within 13 moves.
As all the discussion was about 1. ... gxh5 (and that rightly so), @iceblue found the fastest solution against that move. Of course white wins also against every other black move.
And white wins (even if only after 1. ... gxh5 there follows a spectacular checkmate).
And white has a clear advantage.
Clear advantage isn't a win and it could take more than 13 moves.
It is a winning position, black will lose for sure.
The only critical move is 1. ... gxh5, because after every other move black simply has lost the knight, while his position is still bad. Therefore it is logical and most interesting to examine first what happens after 1. ... gxh5 which ends in a forced checkmate. Nobody wrote that white will always win within 13 moves.
You wrote the "Fastest solution". I can find a faster solution if I played both sides.
As all the discussion was about 1. ... gxh5 (and that rightly so), @iceblue found the fastest solution against that move. Of course white wins also against every other black move.
Or
is it a clear win for black?
Its a loss for black. Bishop performs better than Knight in open games like this. Besides, White also has better position and material advantage.
Right, especially as the knight is trapped anyway in his variation ... :)