"a compulsory contribution to state revenue ... added to the cost of some goods, services, and transactions"
A license fee, be it for a dog, cat, or television
1) Is not compulsory
2) Is not added to the cost of anything
And in the case of a UK Television license it doesn't go to the state.
I think the problem is getting hung up on the definition of tax, which itself is a rather meaningless debate. The UK government, and indeed parliament, has no say over the BBC budget or income, only the level of the license. If a million more houses decided to license a tv set, BBC income increases by £150m, if a million more houses "cut the cord" and just watch netflix, disney, etc, then BBC income decreases by £150m.
Compare with primary/secondary education, where the government decides how much money to spend on education each year. It could increase it one year, decrease it the next, it's a government funded service.
Trying to define the BBC funding model as "tax for a government department" or "not a tax to an independent company" is itself problematic, the BBC is pretty much unique in its funding model and its control. It's overseen by a board which comprises of zero members of government, although the chair and some non-executive directors are appointed by the government.
EDF, the energy company, is owned by the French state, but I don't think people consider it to be government funded.