After 9...0-0 it is very close to a good for Black transposition to Dragon Sicilian. I believe the Bpair is worth the pawn temporarily. The strength of 6...g6 is that it forces White to play 7.Bxf6. If he doesn't he still gets a bad variation of the Dragon.
Thank you for posting the game. I am still too new at posting games
https://www.youtube.com/watch?v=mCRqzl7gY1A
The above is the GM Yasser Seirawan analysis of the game:
Karjakin vs. Caruana R14
I have reviewed about 14 videos and none of the analysts mentions the move 6...g6. After the moves 1.e4 c5 2.Nf3 Nc6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 d6 6.Bg5 several alternative moves are mentioned for Black with some light analysis. GM Seirawan describes the tie break situation that Caruana was facing. He had to win this game( he had to asssume that Anand would not win his game) in order to win the right to face GM Magnus Carlsen for the world championship. If he drew this game then Karjakin would beat him out on tie break points.
Why not play 6...g6 and force GM Sergey Karjakin out of his preparation and make him play chess against GM Fabiano Caruana.