"I am paying for your beverage."
Translation:Dein Getränk bezahle ich.
It's not. Grammatically, "bezahle" is more comparable to "buy", in English. It's like saying "I'm buying for your drink." So that doesn't work. The confusion comes from the fact that Duolingo translates "bezahlen" to "paying for". They expect you to think of it like this:
[I] [pay for] [your] [drink] = [Ich] [bezahle] [dein] [Getränk]
[Ich] [bezahle] [für] [dein] [Getränk] = [I] [pay for] [for] [your] [drink]
It isn't explained very well in the lessons, but that's basically how it works.