It could be based on context. If you have a cup of coffee in front of you and it looks untouched and a plate of food, an english speaker would ask "Are you drinking the coffee?". Same as if you have a little bit left, and I want to take it to the kitchen to wash up. I can ask "Are you drinking that?" "Are you done with that?" or "Are you drinking the coffee?".
It is grammatically correct, but you are right in the fact no one really says it. Think of it more as learning sentence structure! I don't think Norwegians would really say "Drikker du kaffe?" Someone can correct me if I'm wrong, I don't know for sure. But a few of their sentences make very little sense when directly translated. :p
English isn't my mother tongue.
The same problem arouses in courses from German though. A moderator said they took care that the sentences make sense in the learning language, and that makes the German translation sometimes very awkward.
I could imagine a special situation though: Are you drinking the coffee? - extreme astonishment because the coffee is so bad. Would that work in English?