I see.
The guide you followed installs the server as a service directly. Thus there is no real tty output and you don’t receive the password.
I would do the following:
sudo service teamspeak stop
sudo -u teamspeak /home/teamspeak/ts3server_startscript.sh start inifile=ts3server.ini serveradmin_password="ThePasswordYouDesire"
wait for it to fully start and then press Ctrl + C to stop the server again.
sudo service teamspeak start
Now the new password should be set.
