Error in lesson ABC002 "Bronstein strikes! - Part2"

http://www.chess.com/chessmentor/view_lesson?id=5791

After 1...Nf3 2.h3 the mentor refuses 2...Rxg2 and only accepts 2...Rg3.

2...Rxg2 3.Kxg2 Qg6+ 4.Kh1 Qg3 is as clear a win as is 2...Rg3 though.

How is this game over? The white king is note even in check and he can just take your knight with Bxf3 or Rxf3.

This makes no sense at all.

 After 5.Bxf3 exf3, mate on g2 is threatened. The only pieces with access to g2 are the knight and rook on f1. After 6.Rg1, 6.Qxh3 is mate. After 6.Rf2 6...Nxf2 is mate. After 6.Ne1, 6...Nxe1 and its mate in however many moves.

Didn't notice the pawn on e4.

EDIT:

 White has a resource that prolongs the game.

nope, after 6.Rg1 black simply mates with 6...Nf2#

Good catch.
Is the ChessMentor mate quicker than your proposed mate? Usually it won't accept mates that are 1 or 2 moves slower. 

Not completely sure but I believe both are pretty much equally quick. Would probably have to double-check it with an engine though.

In any case - even if "mine" would be one or two moves slower it should never be refused as wrong but at least accepted as "alternatively correct" (or so). The mentor system has such an option for this very case.