I consider myself a gamer, too, though I've fallen behind a little and am a touch more 'old school'.
1. We do hate losing, but it's better that you play honestly; just make it clear that you are pretty damn good at playing Borderlands 2 compared to the average person.
2. You should find one of the games that he likes to play that you don't play that much and try that with him. For me, I would think it cool as hell if my girlfriend wanted to take turns playing Castlevania III. I'd even enjoy watching her play a single player game that I'd cleared and enjoyed (though I would be tempted to give away secrets and be a bit of a backseat player).
3. I have no idea what all of the things are that I want from a girlfriend. The biggest thing for me would be that she is able to hang out with me as a friend but is also able to get much more intimate than a friend. I want to marry a girl whom I feel comfortable spending the rest of my life with and is more than just a good friend.
4. I don't know all of the things, but I do know a few:
-If she never let me hang out with my dude friends
-If she never liked trying new things with me
-If she stopped caring about her personal appearance/hygiene
-If she refused to evolve as a person / had no ambitions in life
-If she didn't want to have sex with me like EVER (I'm supposed to marry a girl who doesn't even want sex? Ugh, I'd rather marry my best friend if that was the case.)
Well since you're both competitive, why don't you try playing more co-op games like left for dead, resident evil, dead island, halo, etc. And you should try each others' games. I find that a lot of people just find a few games that they really like and don't really try many others.
You could play Battlefield 3, it's a pretty good game for teamwork. I.E. Helicopter Pilot/Gunner, Tank Driver/Gunner, Scout Helicopter Pilot/Repair Man, Repairing Vehicles, Giving Ammo, Reviving/Healing, Scanning for enemies, and so on. There are a lot ways to use teamwork in BF3. There's not really as much in CoD. If he was more into Dead Space you could play Dead Space 3 together. It's hard to go wrong with Co-Op games. You could also try Left 4 Dead 2 if you haven't already.
Things I hate when I play with someone is if they Quit out of games all of the time especially after just joining them, unless the server is lagging or if the team is losing drastically right at the start. I also hate people who rage too much. It's okay to be a little frustrated, but when someone is yelling 24/7 and is constantly pissed off it's not really fun to play with them anymore. I have a friend who does both of these things and I try to avoid playing with them because it gets real old real fast. I play games to have fun, not to have someone yelling in my ear.
I think you are more of a gamer than he is. I don't think he's letting you beat him in Boderlands judging by he's reaction. I would recomend Gears of war 1, 2 and 3 its an awesome game on co-op and I think you both will like it. You are already a perfect gamer girlfriend If you said that you played on the nintendo wii that would of been a diffirent story.
LOL awesome! how does he suck so bad that he's losing to you lmao... I'd never lose to a girl in ANY video games and yeah that's a challenge, but if I was to I wouldn't care I'd just be like "WTF just happened"... unless I lost cause I had retards on my team then, I'd rage at them.