Just for the record, I am aware that I could use a chess engine to answer my question but I would like to figure it out without its help. 
Was it a won position?
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In 365chess.com's database, of the 26 games where 10. g5 was played, White won 75%. White does win a pawn, but I agree with you that your opponent resigned way too early. Actually, Black offers a pawn in the Dragon after 9. 0-0-0 d5 and White usually declines it. Perhaps he got the variations mixed up and, realizing that he would have little or no compensation, got frustrated and resigned.
Why not 10...Nh5 11.ed Nd4 12.Bd4 Bd4 13.Qd4 e6
Warning, this post contains use of Chess.com game explorer and 2 links to master level matches.
Until you played g4, you both played the most played moves either side by the book according to the game explorer. (g4 was #3, after Bc4 and O-O-O - until that point it was a Sicilian Dragon, Yugoslav Attack #2). That said, d5 was a bit of a blunder, all 4 of those games, white won. Be6/Nxd4/Bd7/Bxg4/e6/e5 would be more common (in order).
Look up Semenova Lidia K (UKR) - Rozhlapa Vija (LAT) (1976.??.??)
and Shianovsky Vladislav I (UKR) - Byvshev Vasily Mikhailovich (RUS) (1955.??.??)
for a couple of examples of it.
Thanks for your comments. When I spoke of a DB I meant games played by 2000+ players. I know it is easy to misjudge a position. I was really proud I got a draw against a titled player till I realized I was in fact winning.
I was worried my king was too open and failed to see I was up a piece. I swear it was like a blind spot. Nevertheless, his words made me a bit sad. I guess I should be less touchy although weird comments were a reason why I stopped playing people in live chess. The final nail in the coffin was a player who called me a cheater when I won a bullet game and a day or two later he told me I was a noob who should stop playing chess for I lost badly. I have been playing computers for many months now for they are nice and do not mind when I play terribly after a long day at work. 
I swear I am not just trolling and I would really appreciate your thoughts here for either I am dumb or I have encountered a very strange opponent. Here is the story. I am playing a thematic tournament and my opponent resigned after my move 5.
Since I was pretty surprised he had resigned I asked him why he had done so. I thought it was maybe a glitch or something alike. He replied:"you have rating 1959 and you don't know that you're winning a position?"
I do agree with my opponent that I am quite overrated. I should be around 1750. Nevertheless, although I am not really familiar with the opening I kind of think the position was not too bad for black. He could have played 10...Nh5 or Ne8 and I would have won his d-pawn but I was not winning, was I? I have found the position in a DB and a book and although white is a bit better 1/3 of the games was won by black and 1/3 was drawn. So, am I missing something here?