Saying a game is "DirectX" doesn't really mean much, It's only application layer interface, World of Warcraft is "DirectX" but it also runs beautifully in native OpenGL. As for wine, it's either a hit or miss these days.
Actually it means a lot. DirectX and OpenGL are two completely different API's. It's not as if you run an application and it decides it's going to be one or the other, it has to be written for one, the other or both. Your example of World of Warcraft has renderers for both Direct3D and OpenGL. WoW can run as either on the PC, but since DirectX isn't native to other platforms (OSX for instance) the OpenGL renderer is used for such. The only recourse for a DirectX only application outside of Windows is *emulation* such as that included in WINE or Cedega. By default this incurs a performance penalty, regardless of how slight it might be in certain instances. To the best of my knowledge Sins was not written with an OpenGL renderer so unfortunately there's nothing native about it outside of Direct3D.