I installed minecraft via PPA:
sudo apt-get install python-software-properties
sudo add-apt-repository ppa:minecraft-installer-peeps/minecraft-installer
sudo apt-get update && sudo apt-get install minecraft-installer
And now I can start the login screen for the game on the console with
java -jar /usr/share/minecraft/minecraft.jar
and even copy the running game-screen with
cp -a ~/.minecraft/ ~/mcraft
which allows me to start it without internet connection:
java -jar ~/mcraft/launcher.jar
Now since I don't have an account, how can I start the demo?