A fee does government collects is tax, if it just mandates to be collected by a non-governmental org is not tax.
Government does not get involved in collecting this fee except for having a law that an organization(ARD ZDF Deutschlandradio Beitragservice = joint contribution service for ARD ZDF and DR) can collect fees from every household that uses any kind of broadcaster/receiver devices.
It does not pass through the German government so it is not a tax.
More info: https://politics.stackexchange.com/questions/27856/why-is-th...