There are two kinds of testings for games, and both require different skills:
- Testing for bugs
- Testing for fun
Most professional testers in the industry test for bugs: they look for problems and don't need to give a rat's ass as to whether the game is fun or not. The process is pretty much scientific experimentation, you need to be able to experimentally figure out what the exact conditions for a bug is - say there's a camera glitch, you need some experimenting to figure out that it's only when changing weapons facing a wall; an inferior tester might just say "sometimes the camera jumps when you change weapons". You also need to be willing to experiment with a lot of weird crazy things like going around a hill three times (I once had that - there was a bug with dynamic loading, after three times in the same direction a part of the map wouldn't be loaded) - so a hardcore gamer in the genre you're testing is a plus.
If that's who you're interviewing, maybe you could print out a list of bug reports, and ask him to go over them, tell you which ones might be the same bug, which descriptions aren't good enough, etc. You could also show him a video of a bug / crash and ask him to describe what happened.
I don't think enjoying games is a necessary condition - I'd rather have a very smart and focused tester that doesn't care about games than a gamer with a short attention span that doesn't want to be looking for rendering problems in the same damn half-finished level for weeks in a row. Plus, a non-gamer might try some things gamers wouldn't usually do. Being able to describe why a game is fun or not fun isn't important here (apart from figuring out what kind of games they play). Social skills aren't as important as for other jobs, testing is mostly solitary.
As for gameplay testers - those that test whether the game is fun - a lot of the time, they aren't there long term, they're just students or something that aren't reused. There are also some "experienced gameplay testers" who are more like game designers - their job is more to organize test with users and collect feedback. For these people, being able to describe why a game is fun, what they enjoyed, what kind of games they like, etc. - general game design and criticism skills.