I still don't see where the Bioshock aspect comes in. Just because both have (not closely related) trait systems doesn't mean you can just group them together. Same with L4D - just because games have co-op doesn't mean they're the same genre or anything alike...

Personally, I'd probably call it first-person Diablo with co-op set in a Mad Max post-apocalyptic future. The Diablo bit covers the leveling and loot-getting.