The games don't "support Nvidia" so to speak, it's "Nvidia supports the game". Nvidia, for example with Bad Company 2, supported the development of the game financially to add Nvidia features such as Nvidia Surround etc, same with Batman: Arkham Asylum, Physx were added to it, and Nvidia helped develop code to allow anti-aliasing on the DX9 Unreal Engine, which is usually not possible as you normally need DX10 and above for anti-aliasing on deferred shading renders.
ATI did the same with Dirt2 in supporting the developers to optimise the game for things like Eyefinity. It's pretty much down to which side gets there first.