If you ever hear anyone use the phrase, "I just want someone who doesn't play games!", they don't mean you. They have a particular person in mind who is playing with games with them, they wish this person wasn't playing games with them, but they refuse to give up on said person even though through their actions they've shown they are an untrustworthy POS. Or, they mean they want someone who is celebrity level attractive AND who doesn't play games, not just some regular schlub like them who doesn't.
Face it, we're attracted to who we're attracted to, and you can't logic your way out of that. Also, as a species we are SO fucking stupid it's not even funny anymore. It's more tragic than comic.
So if you hear that phrase from someone, no matter how attractive you find them or how good of a fit you think you'd be together, just say, "Yeah, that sucks," and walk away. Save yourself the time and headache.