The game was 80/d5, In the final position I beleive black has a winning position, but less than a minute on the clock, white while losing had a solid position and had 20+minutes on the clock, also white is rated 1790ish, and black is rated 1380ish. Should black have risked it? or was offering a draw the right call?
Should I have fought on? (Time trouble)
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If you care about what number your rating is, and every point matters to you, then clearly the right thing to do is offer the draw. Because with little time left and a big rating gap, then being honest, there is a large chance you'll screw it up and take a loss of a point or two, whereas you can get a nice little gain if you take a draw.
If your primary concern is something other than what your rating is, well, it depends what your concerned about? There are a lot of possible things one could care about, such as bagging the scalp of your first opponent rated over 1700 (if true). Or pride could factor into it somehow. Or getting experience in a time scramble.
So...no one can tell you what the "right call" was. YOU had to decide that based on what is important to you.
If what you are really asking is whether this is a simple win, the kind of thing that a 1380 player can manage using under a minute, then I'd have to say no, its more complicated than that. Just based on the ratings, position, and time left, I'd bet against you.
I think you should have fought on with Rg6 because this move leads to mate soon. You only have to move your other rook to the h-file and i think that white can't prevent or even delay this very long. If the rook checks you can move your king to the upper left corner and prevent the checks and if white places his bishop on the h-file to interrupt the check you will be able to wi this bishop by putting both rooks on the h-file and the arising endgame should be won even with thirty seconds by winning whites' last two pawns and then pushing the pawns. But your decision definitly wasn't wrong because it is very hard to see easy things with little time- i know that from own experiences and a half poimt againts someone who is more than 300 points higher rated than you is a great success.