Can hunters claim compensations for game that has been killed by wolves?

No, as game is unclaimed, i.e. does not belong to anyone, according to the hunting law (§1 BJagdG). Only through killing game, hunters acquire ownership of an animal. From a legal perspective, hunting is not a line of business. As the return of the wolf is not an act of sovereign power (e.g. as reintroduction), asset values are not affected. Therefore, there is no compensation for reduced income through hunting.