not to typecast, but a gamer who avidly plays CoD and doesnt appreciate a woman trying to meet him halfway doing what he likes is not going to ever appreciate it. good on you for knowing the mark of a repetitive, boring game though.
borderlands and left for dead are FPSs made for co-op, i know those have been suggested already. strategy games really arent good team games; great multiplayer, but of the much less mutually fun variety (competitive). i have endless fun with portal 2, and definitely look into an MMO, since youre actually trying to further a human relationship with it rather than ignore them all
if you want my cold, learned advice though: through all the lonely nerds expressing their love of gamer girls in meme form, gamers really dont make good couples. 2 gamers are too independent, too specific in their tastes, and too at odds when one wants time with the other and they just want to f**king get to the classical era because motherf**king gandhi got there 10 turns ago. it takes 2 gamers with miraculously similar tastes to work, and lets just say the only one ive seen work for an extended period was because he is in the navy and is gone for 6 months at a time, and given what ive seen of my fellow sailors... i REALLY doubt this particular individual was entirely loyal to her.
opposites attract. really: you need someone to balance you out, not someone who makes the same mistakes you do.