1...Rg8 - "Now the game is just about lost, as I now have to deal with two pawns"
Worse than that, White has a mate-in-one. 2.Rd7#
3...Rxg6 - "And I'm saved!"
Actually, White still has a mate-in-one. 4.Ra5#
Drawing a lost game
Sort:
" 3...Rxg6 And I'm saved!"
Not really chap: 4 Rd7#! 
I know, but Max's rook took my rook making it a draw.
Kudos for scoring the swindle--long shots are worth it when you're losing! And this is a common stalemate trick in R+P vs R endings. I was just pointing out those tactical "wrinkles" since they weren't noted in the annotations.
To see the full game, go here:
http://www.chess.com/echess/game.html?id=923231