why does austria have compulsory military service?

Answer 1

Because they can,

Conscription is also mandatory in Germany as well.

And was also in all of the old Communist countries.

In the past, post WW2 it was also in the United Kingdom, Belgium, France, etc...etc....

Answer 2

They have had it for many years. Although they are a neutral country they do make troop contributions to various UN peacekeeping missions organized under Chapter six of the UN Treaty. In fact, they suffered some casualties among their personnel with the UN force in Lebanon (UNOFIL). During the NATO operation in Bosnia they contributed a transport company as well.