After reading a bit more, it appears that DirectX 11 is supposed to be backwards compatibile for everything, and apparently Windows 7 automatically installs it anyway. So, I'm not sure whether that would solve your problem or whether you'd be able to remove it even if you wanted to. Since it's happening on multiple games though, it definitely sounds like some kind of driver issue. I would recommend browsing ATI forums for driver problems with those games and/or Windows 7.
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