I am trying to backtrace my steps, this is the following what I did:
1) Downloaded the linux version on
Yahoo! Zimbra Desktop
* as a normal user*
2) made the file executable: chmod 755 zdesktop_0_92_build_1418_linux_i686.sh
3) run the file: ./zdesktop_0_92_build_1418_linux_i686.sh
pls note the . before the /
4) in my case no desktop icon was made, so I made one.
thats it..it runs like a charm.

Only two items are missing:
- possibility to autostart in the background (dont know how)
- Zimbra doesnt install itself in the Aplication menu (minor detail)
Let me know if this helps
Cheerz
Bloemetjesgordijn