In order for the launcher to run, it is necessary to install the
Microsoft .NET Framework 2.0.
Currently Wine-Mono does not work as a substitute.
For the Retail version you can bypass the launcher by running TS3.exe instead of the launcher.
For the Steam version you MUST install .NET, as the binary cannot find Steam unless it is launched from Steam.
On the Steam version, the first run MUST be run through Steam, using the launcher so the DRM can initially register the install.
After that you can run by using TS3.exe, like the Retail version.