Don't edit .so files! They're usually binaries, not text (although some libc.so's are just text files telling the loader to go look somewhere else for glibc, but they're the exception).
You didn't pass --enable-opengl to ./configure? Try doing that. You shouldn't need to make uninstall, just make distclean, then ./configure --help (to check for other interesting options you might want to enable), then ./configure --enable-opengl <any other options you want>.
You are right, having make depend and make on different lines is no big deal. The shell "&&" construct tells the shell to execute the second command only if the first succeeds, which is what you effectively did anyway. My guess is that you need to pass --enable-opengl.
Also, check the output of the configure script manually -- if it says something about "warning!!! you are explicitly linking against a thread-safe OpenGL!" or similar, then try replacing your /usr/include/GL/gl.h, /usr/include/GL/glx.h, and /usr/include/GL/glxtokens.h with the corresponding files from the NVIDIA_GLX package -- they will have been installed in /usr/share/doc/NVIDIA_GLX-1.0/include/GL, so just copy them from there to /usr/include/GL (but rename the others first!).
If you don't have a /usr/include/GL directory, then use /usr/X11R6/include/GL instead.
Once you get the "thread-safe OpenGL" message to go away, you should be all right. make depend all install should build the dependencies, then the full wine binary, then install it, in order.