you seem to mix up something. termination with advance notice is a normal process and pretty much always possible. i doubt there is any country in the world where you can't terminate employees with sufficient advance notice. the periods for advance notice differ but the process is otherwise the same in austria or in germany for example. and i am pretty sure most EU countries are similar. i only heard about france having much stricter rules for termination. so how is austria worse in that regard?
in this particular example, the legal date for termination in austria would have been december 31st (because by default it is 6 weeks notice after august 26, to the nearest quarter)
in germany it would have been september 30th.
and for termination without notice
https://www.arbeitnehmer.at/kuendigung/entlassung/
pretty clearly spells out the reasons when someone can be fired, which contradicts your claim that people can be fired for no reason.