"I am paying for your beverage."
Translation:Dein Getränk bezahle ich.
the English "pay for" suggests the dative
It does not. "(to) pay someone" (i.e. someone is the recipient) may indeed suggest dative but "(to) pay for something" does not. The point is moot anyway since English does not have those cases.
the grammar is more akin to "I'm buying your drink".
Actually, in English we pay bills, dues, debts and taxes. There is no rule that requires "for" with the verb "to pay" in English -- it just so happens that we use it in constructions like "to pay for goods/services". We could have just as easily talked about those the same way we talk about bills or dues.