For me, gamer means someone who is actively interested in my hobby themselves. No direct personality pops into mind but usually it leans more towards "fun spirited" considering that games are meant to be fun. Now, if you then tell me you almost exclusively play CoD AND other FPS's, it shifts - just as it would shift if you told me all you play is RTS's. However, both of those tend to shift to a similar area. That is, to a place where you don't really have a focus on games so much as you have a cubby hole you stay in and explore 1 game type. This can be a hindrance on me as I don't care for FPS's or RTS's so if that is your cubby game type, we have little to discuss. I see your gaming habits are competitive in nature and mine aren't so while I enjoy competitive games from time to time, you pretty much get your "fun spirit" from being competitive. No problem, to each his own.
Now, suppose I find out you play mostly city/empire builders or simulators I don't see you as competitive, I see you as constructive. I do have a strong link to those types of games myself. I have plenty to talk about with you once we have found a game we have both played and probably liked.
This goes on for many genres. Each tell me something different about you. Most often I find out that people are interested in a large sample of a few genres. Like RPGs, Action Adventure, and FPS's. Perhaps Racing, FPS's, and Fighting Games. While they are always disappointed to hear I don't care much for FPS's we bond over the other genres and the few FPS's I actually enjoy sparingly. Everyone loves them some FPS's and I let people down a lot on that one. FPS's, Fighters, and Puzzles just arent for me. I don't mind puzzles if in an adventure game or something but like Tetris? Zuma? Even Plants vs. Zombies? Yeah - I'll pass.
SO for me, being a gamer just means you are fun spirited and not as dull as people who (IMO) just want to sit around and stare at other people do stuff (TV).I am happy to sit my butt down and break out the Monopoly board with others over going to sit in a movie theatre and watch the same tropes get told to me in a different way. There are movies I love, but I would rather spend my time interacting with my entertainment and I assume others are the same way. It means you want to be involved which to me means you want to be part of the fun.
As for the whole "play a game, you are a gamer" thing, I wouldn't call someone who plays Solitaire a gamer. That isn't me being a douchebag elitist, that is just me requiring your lifestyle actually involves gaming, not a game. Old ladies who go play Bingo on Friday night aren't "gamers", they play a game. If all you play is CoD, you aren't a gamer, you happen to play a game. A gamer has gaming (at least a genre) as a part of their lifestyle. You play a lot of card games? I see you as a gamer. You play board games? Gamer. You played a game one time in your life? Sorry, but you don't qualify, the bar is low enough as it is.
