Thanks dfreer. This solution from another thread solved the permissions problem, and I can now launch as a regular user (thanks to Grishka):
This answer also solved my 'error while loading shared libraries: libGL.so.1' problem:
1. kill pulseaudio (sudo killall pulseaudio)
2. run pSX as root (sudo ./pSX)
3. find the "sound" tab in the configuration and switch the "device" setting from "default" to your soundcard (plughw:0,0 in my case). apply. close pSX.
4 open /root/.pSX/psx.ini in a text editor (gksudo gedit /root/.pSX/psx.ini). find the "device" string under [Sound] section (I have "b7d317a4" there).
5. paste this string into the relevant section in ~/.pSX/psx.ini, in place of all zeroes. save. if you don't have this file in your user directory, run pSX and cancel just after choosing language, on the bios selection screen. pSX should save settings then.
now pSX runs fine even after reboot.
Try this only after verifying that you do in fact have the identified files in the stated locations.
sudo unlink /usr/lib/libGL.so.1
sudo unlink /usr/lib32/libGL.so.1
sudo rm /usr/lib/libGL.so.1.2
From there I reinstalled IA32 libraries using synaptic.