If you don't want to mess around with the copy of atioglxx.dll in the System32 or SysWOW64 directory just paste the file into the folder your broken application is installed in. It fixed Anachronox for me :]
The atioglxx.dll solution did not work. I ended up uninstalling the 10.6 driver and reverting back to an older version.
Before I did this, I tested a few other games. Looks like Catalyst 10.6 breaks the following games: Return to Castle Wolfenstein, Jedi Knight Outcast, Quake 2, Quake 1, Hexen 2... Quake 3 actually worked which was kinda strange since RTCW and Jedi Knight Outcast are built using the Quake 3 engine.