Do you have HKCU/Software/Wine/Direct3D/DirectDrawRenderer set to "gdi" perhaps? This disables D3D support altogether. You could try with a fresh .wine, it should run 3dmark2000 and 2001 out of the box.
I tried latest WineHq, it created ~/.wine directory and installed 3DMark2000 correctly, however when I try to run I get same complains: "3DMark needs DirectX7 and proper drivers installed". Also, this is printed on console:
cxtest@mpilka:~$ ~/cxtest/wine/wine ./.wine/drive_c/Program\ Files/MadOnion.com/3DMark2000/3DMark2000.exe err:ddraw:DDRAW_Create Couldn't load WineD3D - OpenGL libs not present? err:ddraw:DDRAW_Create Couldn't load WineD3D - OpenGL libs not present? err:ddraw:DDRAW_Create Couldn't load WineD3D - OpenGL libs not present?
Note ~/.wine directory generated by Wine does not mention HKCU/Software/Wine/Direct3D/DirectDrawRenderer key at all. Also, glxgears runs fine, xdpyinfo says GL is there (ATIFGLEXTENSION, ATIFGLRXDRI, GLX, SGI-GLX extensions are present).
Martin