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The modern Austrian government fears the Habsburgs because it understands rightly that it is illegitimate two times over. Now if the FPÖ were to be in charge, perhaps that would be another matter.
In any event, The wording of the article suggests that the claim was presented under the wrong jurisdiction, rather than that it is denied without recourse. Perhaps the claims should be pursued through EU administrative channels.
If Jewish emigrants can make claims against Germany and Austria on the basis of being "Holocaust Survivors" then certainly the Habsburgs have a right to make a claim for restitution on the same basis.
Unless, that is, there is one law for Jews and another for Gentiles.