With rook on g1, 13. gxh5 gives it a direct open file against the king.
Wrong! The black king is not on the g file. It is on the h file and the rook on f8 is ready, if required, to come to g8 and fight for the open file.
g5 allowed 13... Bg4, necessitating 14. Rxg4, an exchange sacrifice for the attack to continue.
Again, wrong. 13... Bg5 14 Rxg4 hxg4 ...