I have been playing some ARAM under custom games recently, and I'm a level 29. I have 67 games listed, so I'm assuming that this is solely the SR games that I've won?

I typically play Dominion, so I know that it'll show much less for SR. I just wanted to know why it did this. I don't see how the total number of SR games is THE deciding factor when I have 80ish Dominion wins and several TT wins as well. Anyone know why this is the way it is?

It is this way because the majority of the community only cares about SR. SR is the map for all tournaments and is played more often. Very few people care about your wins on other maps because those maps are generally played for fun or if you don't have an hour to play a match on SR.