Translation:The guest drinks tea in the living room.
If 客人在客厅喝茶 = "The guest drinks tea in the living room", then how would you say "The guest in the living room drinks tea" in Chinese?
In the first case, it answers where the guest does the action of drinking tea. The second case just points out that specifically the guest located in the living room (not any other guests elsewhere) drinks tea in general (as opposed to coffee or anything else).
If English can make a grammatical distinction between "The guest drinks tea in the living room" and the "The guest is drinking tea in the living room" then so should Chinese. My understanding is that the verb by itself is the present habitual 'drinks', and needs something like ‘在' to make it progressive. Am I wrong with this?
Yes and no. You're studying German, so you know that "the guest drinks" and "the guest is drinking" are both "der Gast trinkt", and there's no present progressive tense. It's the same in French, though there are different constructions that can make it clear that the aspect is progressive, if necessary.
Likewise in Chinese, the bare verb may or may not refer to a continuing action, depending on the context. Also, there's already a "在" in this sentence, and to me it would be weird to add another, but I have to defer to native Chinese speakers on this.
I think you could use "喝着茶" ("hēzhechá") to express "drinking tea", but I'd like to hear from a native speaker as to whether this would be necessary or natural-sounding.
The present imperfect tense would make a better translation, i.e. "The guest is drinking tea in the living room." It suggests that the guest is currently drinking tea in the living room.
"The guest drinks tea in the living room" sounds awkward in English because one would only say that to indicate that the guest prefers to drink tea in the living room instead of some other room.