It seems like TeamExtremeMc is gone for good and server operators have no intentions of starting the server back up. Sadly with that their Launcher is also gone.
Of course there are still some old versions of TeamExtreme Launcher around but they're not updated anymore so in most cases latest versions of Minecraft won't work.
The only alternative launcher I was able to find was this Launcher: ExtremeLauncher
Looks like it's still working and also all versions of Minecraft are supported.