Unfortunately, my knowledge of games is mostly limited to Nintendo consoles since I'm actually a big Nintendo fan -- and they have a nice stance in regards to fan-related things (see starmen.net's Mother 3 book). On top of all that their stuff are easier to make into art since they have a long, rich legacy (it's also why Smash Bros. can exist and be hugely successful -- gameplay aside). Plus, the artists themselves are familiar with the games. Bobby O'Herlihy was able to put out that, in my opinion, great Pikmin-inspired print because he's actually played it. and yeah, I want to promote Nintendo's stuff too -- cause I'm most definitely a fan and want them to do well (hence the pre-requisites), but I also want to reward fans as well (hence the pre-requisites).
With third-party titles I haven't researched but I know Sega is something that shouldn't be touched with a ten-foot pole... Sony is likely to put stuff out their own screenprints as well (ratchet & clank, the last of us).
What games would you like to see though? This thread also has a gallery co-owner here: deadbolt1388. Bottleneck gallery puts out awesome themed shows every month. So even if I can't make it happen (as in do it justice), deadbolt might be open to ideas.