The error was:
libGL error: failed to load driver: swrast
libGL error: Try again with LIBGL_DEBUG=verbose for more details.
1. Despite the fact that I installed the 64-bit version of the Google Earth RPM, it's actually 32-bit and needs 32 bit OpenGL drivers
2. With the proprietary ATi drivers installed, the default libGL.so library (/usr/lib/libGL.so.1) is incompatible with the display, yet this seems to be what GE is trying to use.
3. GE will use anything in it's own directory FIRST, evidently
So, I ended up copying /usr/lib/fglrx/fglrx-libGL.so.1.2 to /opt/google/earth/free, and made symlinks to it as libGL..so.1.2, libGL.so.1 and libGL.so in the same directory. Now it works.
I really, really wish that Google would get their shit together with the 64-bit versions of Google Earth. I'm running fast, clean 3D graphics on this workstation every day, and no other programs ever seem to have problems like this. Why in god's name does it have to be so picky about where everything is located, and, well, who runs 32-bit anymore?