Can't see the game you were supposed to post, but this might help to answer your question http://www.chess.com/article/view/the-greatest-amateur-game-of-all-time
Can the average player have a brilliant game?

[Site "Chess.com iPhone"]
[Date "10/10/2015 10:34PM"]
[White "HubbaBubba907 (1322)"]
[Black "Hannahdog22 (1271)"]
1.e4 c5 2.Nf3 h6 3.e5 d6 4.exd6 Qxd6 5.d4 b5 6.Bxb5 Bd7 7.Bxd7 Nxd7 8.Nc3 Ngf6 9.dxc5 Qxc5 10.Be3 Qc8 11.O-O Ng4 12.h3 Nxe3 13.fxe3 e6 14.Qd4 Bc5 15.Qxg7 Bxe3 16.Kh2 Ke7 17.Rfe1 Bf4 18.g3 Rg8 19.Qd4 Bxg3 20.Kh1 Bxe1 21.Rxe1 Qb7 22.Nd5 Kd8 23.Qh4 f6 24.Nxf6 Qxf3 25.Kh2 Qg2# {Hannahdog22 won by checkmate}
I had a look through your game. Out of the opening, white is left with a pawn advantage, better development and a safer king. I would call it a winning advantage for white as long as he avoids getting into tactical positions where black has counterplay.
Up until 18. g3?, white seems to have a comfortable lead. With 18. Kh1 I think the black king would be the king in danger. 18. g3 ignores that black has great control over the black squares and gets you back in the game. Perhaps white can play 19.Rxe6 Kxe6 20. Re1+ Be5 21. Rxe5 Nxe5 22. Qxe5+ to get black king in the open and still hold the game. The position is then unclear, but I would think that white could get something like a perpetual check.
Your attack after that seems solid, but isn't spectacular either. I would be careful calling this a brilliancy since it implies that there is little room for improvement for at least one of the sides. In fact, if you want to improve, you should acknowledge that the game wasn't brilliant and rather try to find and learn from your mistakes

http://en.lichess.org/ctPhFhiS#0
I think that any game that starts with 1. e4 c5 2. Nf3 h6? 3. e5? should not be considered a game at all.

Hmmm. Don't remember calling this game brilliant, just that I did quite well. I appreciate the analysis. I guess my point is, when we analyze the games between the masters, when we look at the losing side, aren't there mistakes there as well? Or we do we just say, "well, they were brilliant. Just less brilliant than the victor."
Can the average chess player have a brilliant game?
I've written on this subject before, and almost overwhelmingly the response I get to this query is an emphatic "No!" But I disagree. I make my analogy to my days when I played golf (I find there are a lot of commonalities between these two activities). I enjoyed golf, and got myself down to a four handicap. Respectable, but certainly not a threat to join the PGA tour. However, I did on occasion have truly unbelievable rounds, the kind that lure golf players back to the course with the expectation of continued success. Once, I had five birdies in a row. Another time, I shot a 3 under par 69; two other times I had hole in ones.
So is it possible for the average player to experience a moment of clarity where their chess game is on par with a grand master? I believe it is possible. But just like my great rounds of golf were always at some point followed by disasters, these moments are not sustaining.
There are several possible reasons for this, of course. Every one's brain works differently. The brain of the masters are much less likely to "missfire." This can be due to inherent ability, or years of a disciplined training regimen, or both. There's a new show on CBS right now called "Limitless," where the protagonist Brian takes a pill that allows his brain to work at 100% efficiency. They call such pills nuero enhancers, and the opening episode showed our man Brian cleaning up at the city park against all the chess regulars. Would such nuero enhancers threaten the legitimacy of chess tournaments? Certainly, but that is for another discussion.
Back to the matter at hand. Can an average player have a brilliant game. When I was at the Chess museum this past fall, a very nice young lady working there explained to me that the masters call us regular folk "woodpushers." Such snobbery! Generally speaking, I do find that the higher that rating, the more likely one is to look down upon those whose ratings are lower, all the while being secretly envious of those who have attained loftier numbers. So I submit a game I played today, one which I thought I did quite well in by starting off with a pawn sacrifice, the title by the way for the recent movie about Bobby Fischer's showdown with Boris Spassky for the world championship of chess. As you review the game, try to do so open minded. All too often I see higher rated players dismiss these games when they uncover the mistake of the loser, thus discarding the game as a mere exhibit of those "woodpushers." But if you removed the names, and inserted albeit fake names and ratings, would they judge it quite the same? I think not.