I downloaded the deb (amd64) package and tried to installed it through "Software Install". That didn't worked so I tried the dpkg -i command instead. That threw the following error:
chmod: cannot access '/tmp/tuniqueinstance*': No such file or directory
dpkg: error processing package tmetricdesktop (--install):
subprocess installed post-installation script returned error exit status 1
However, after installation it did open a prompt which asked me for my username and password. After I entered my credentials it showed me another popup asking me to continue tracking my time on the active item. I pressed OK, but than nothing...
When I tried to open the program again it started complaining about a /tmp/tuniqueinstance file. Pressing OK had no effect. After that I tried to reinstall it again. This time I encountered no errors, but still nothing happened when trying to open the program.
So unfortunately no desktop client on Ubuntu for me. If it's of use, I'm able to send some log files.