After 8. Nxb6 axb6, white is more or less forced to play 9. Bb2 anyway. With the bishop gone, d4 is no longer hanging, but after other moves, 9. ... Nxb4 could be a threat due to the pin of the a-pawn (10. axb4 Rxa1). (Of course 9. c3 would also prevent Nxb4, but that is clearly inferior)
After 9. Bb2, Black will make his 9th move, which could be 9. ... Nf6, 9. ... Nce7, 9. ... Nge7 etc. (though the last one looks quite bad now, because the knight on c6 has nowhere to go).
If white plays 8. Bb2 first, black of course cannot reply 8. ... axb6. He can also not prevent 9. Nxb6, so he will make another move. 8. ... Nge7 and 8. ... Nf6 look reasonable, possibly also 8. Nce7 (although d5 might be an idea for white - however as you can see these are the same moves black would have to consider on his 9th move if white took right away).
Anyway white can now see how black continues, and then decide whether or not to take the bishop on the next move. In the game, 8. ... Nf6 happened, after which white decided not to take the bishop. This is reasonable, because taking the bishop right away is better after Nge7. He didn't even take after 9. c4 a6, although 10. Nxb6 axb6, as pointed out by Brian, is probably an option. After 10. g3 however he got a very good game due to the useless black bishops, but on his 13th move, white blundered with a strange rook move (13. Ra2??) that doesn't seem to make any sense (13. Nac3 followed by Nxe4 would have been the correct idea, or 13. c5 possibly followed by 14. Nac3), and was worse, but later managed to escape into a drawn ending (it is good to know that rook+rook pawn + bishop pawn (on the same wing) vs. rook is usually a draw!)