actually he can because after 22. Bxg2 Rxd1 23.Rc8 is winning for white.
Before making a move... look for a better one!

White CAN take the bishop, if you capture his queen he will MATE you on the back rank with his rook.
1.Bxg7 Rxd1??
2.Rc8+ Rd8
3.Rxd8#
Lesson? STOP AND THINK BEFORE YOU POST.

I don't think Black has better than 21... Kh8 then maybe White plays 22.Qf3 and I think Black is simply down a full rook with nothing to show for it... Black is lost.
So I think this novice has learned his lesson. Here is the game:
Here is how it COULD have gone:
At this point, white can't take with his bishop, because I can take queen with my rook. Also, if he doesn't move rook, I take it, so when he does, I move the bishop to f3, revealing a check and attacking the queen with the bishop. I take the queen, and the game would have been a different story.
The lesson? STOP AND THINK BEFORE MOVING.