Looks like all that is happening is that the driver you downloaded from ATI is trying to install it's own version of the LibGL library.
libGL is I believe what is used for OpenGL rendering. Nvidia has it's own version that it installs, but I don't know what ATI does.
Library files are pretty much the same thing as *.dll files in Windows. What they are, basicly, is a collection of functions that are used buy a veriaty of programs. So that instead of each 3D program having to have it's own 3d rendering technics or using the same code over and over again in different programs, the program just calls on that library and pulls a command/function from it and excecutes that instead.
Plus if any programmer figures out something new, faster, bug fixes, or whatnot then he can stick that into the library and all the programs that use that library can benifit without having to rewrite everything.
The bad part is that some newer libraries are only somewhat compatable with older libraries, or that newer programs depend on newer versions of the library that have features or bugfixes that the old ones lack.
That, along with various programs and tools, stuff like this are called dependances, and were a big issue with Linux until now when they started using good package managers like Yum, urpmi, and apt-get to keep track of all the changes.
What I would do to try to fix your problem is to move the /usr/X11R6/lib/libGL.so.1.2 file to a safe place for safe keeping, and then try installing the drivers. You may need to "force" the install if it complains about it and that will probably cause the installer to ignore the problem. For rpm stuff maybe try "rpm --help" or "man rpm" to find out how to do that.
Also check out the "symbolic links" to that library. Symbolic links are like shortcuts, but more fundamental and involves the filing system. Often with libraries you have several symbolic links, because maybe libGL.so.1.0 was older, but still compatable with libGL.so.1.2 (for example)
So you may run into programs that still expect libGL.so.1.0 to be present so instead of making a bunch of copies of the library file they just make a symbolic link to the newer version of the file.
"ls -l" will show if the files are symbolic links. Try going to /usr/X11R6/lib and use a wild card to see if you can find all the files that may be linked to the libGL.so.1.2 file.
Like this:
ls -l libGL.so.*
Now as long as the libGL.so.1.2 is the "real" file then you'll be ok.
You can make your own symbolic link with the "ln -s" command. See "ln --help" and "man ln" for help. You can also make "hard link" which is the actual pointer to a file on the harddrive. Each file has one hard link, which is it's name. It can have more then one name, though.... But symbolic links are much safer.
Now all this is just to be safe. More then likely you can just delete the offending file, install the driver and then have about a 90% chance of it working fine.
Also don't forget to make sure that your X windows is properly configured.