https://bugs.winehq.org/show_bug.cgi?id=38216
--- Comment #16 from Andrei Slăvoiu ansla80@yahoo.com --- <Renderer>ATI Radeon Turks XT Prototype OpenGL Engine</Renderer>
That explains why it's not recognized, so indeed you are hitting the fallback path. The old fallback code was able to recognize your card as capable of at least DX10 based on the presence of EXT_GPU_SHADER4, but the new code that uses the shader capabilities no longer has access to the list of OpenGL extensions.
And since the problem will be solved the right way by using core contexts (work in progress) I doubt anybody will be willing to workaround this cornercase until then.
The only solution for now would be to add the renderer string for your card to cards_amd_binary array in dlls/wined3d/directx.c It should like: {"Turks", CARD_AMD_RADEON_HD6600},