Why does Stockfish prefer white in this position?

After 8...Be4 the engine recommends the move 9. O-O. But after 9. Nh4 Bxg2 10. Nxg2 Bxd4, white only loses a pawn instead of trading a rook for a bishop. I don't see any immediate advantages for white, so I assume it has something to do with the position of white's pieces versus black's. Or maybe because white has more active pieces? 

Strong center--and about to get stronger after Qd3 and a pawn push to e4,, active pieces, powerful unopposed light-squared bishop, Enough to more than compensate for the exchange. But there's plenty of play in the position

Thanks for the insight! Seems like a position I can further analyze, and I know understand the advantage white has in the position.

Actually, I like 11. c5 bxc5 12. a3 Ba5 13. dxc5 threatening to trap the Bishop with 14. b4. If Black is really forced to play 13. ... c6 in order to rescue it, then he looks to have a horrible game, exchange up or not.