A true gamer shouldn't judge a book by it's cover (Or rather, a game by it's graphics). A gamer should judge a game by the sum of it's parts, starting with gameplay, moving to controls, story, interaction (Community, "addiction"), flaws, then aesthetics (IMO). Having better graphics will make the game "better", but if the gameplay stinks or the controls make it impossible to play, then you got a pretty piece of crap.
Also, a gamer isn't someone who plays a verity of games (Though most gamers do), but a gamer is someone who sets aside time to play games (Usually whenever they get a chance) because they enjoy them that much. For example, one of the first games I ever played was Pokemon Red when I was 4/5. I played it whenever I could, though I could barely read. Because I enjoying it so much, I ended up getting a N64 a year later. That transitioned into PC gaming along with getting a GC. My Gameboy Color was replaced by my GBA, which was replaced by a DS and multiple PSP. My GC (Which will never truly be replaced) moved over for the Wii, and then an Xbox 360. So when was it that I became a gamer? I'd like to think it wasn't when I bought a system/games (Because anyone can do that), but when I played Red version late at night, grinding my Pokemon, not for achievement, but for the love of the game.