Try this in a terminal:
cd ~/
wget -c http://qudos.quakedev.com/tmp/Paintball2_build017_full_linux.run
chmod +x Paintball2_build017_full_linux.run
sudo sh Paintball2_build017_full_linux.run
When the installer is done, if it asks you if you'd like to run the game, select no. (Most loki installers ask this, I'm not sure if this one has it set up like that, I forgot)
If you already ran it right after the installer, then it was run with sudo, so the permissions on your user's files are owned by root, which might explain it not running, I'm not sure.
To fix this do: sudo chown -R <user> ~/.paintbal
where "<user>" is your username.
Then try running paintball2 from a terminal, if it gives you an error, post it back here.