"He drinks red wine as often as possible."
Translation:Li drinkas ruĝan vinon kiel eble plej ofte.
Yeah, I agree trinki should definitely be accepted here. There seems to be some ambiguity whether drinki implies "get drunk on", "drink alcohol to excess" or whether it's just a special version of trinki that applies to alcoholic beverages. To whatever extent it means the former, trinki is more acceptable even than drinki, since the english sentence doesn't necessarily imply that he's drinking a lot of red wine as often as possible. But even though http://www.reta-vortaro.de/revo/art/drink.html cites PIV2 as saying "drinki = trinki alkoholaĵon en nemodera kvanto", there's a note from Sergio Pokrovskij contesting this interpretation, pointing out that the activity that happens in a bar (= drinkejo) is not necessarily excessive (but of course it does pertain to alcoholic drinks)