The sentence is written in a conversational style, even though it is in a respected publication like Smithsonian Magazine.
You can tell this because of the contraction "let's". Many people were taught in school that contractions should be used in speaking (and dialog) but not in formal writing.
The word "geography" is functioning as the object of the verb talk.
It would be more formal (or "more correct") to say:
If you put in a different noun (television) or pronoun (you), you'll notice that these "about" phrases are also acting as the object of "talk".
None of them is an adverb.
It is an acceptable idiom in conversational English to drop the word "about" in some of these sentences:
Yes: Let's talk geography.
Yes: Let's talk television.
Awkward: Let's talk you.
The last one is very awkward, and very informal. It's pronounced the same way as "let's talk about YOU": "let's talk YOU", not "let's TALK you", and not "let's talk, you."
You can write it in quotes to make this more clear:
Still awkward: Let's talk "you".
Still awkward: Let's talk "you" for a moment.
You can always leave the word 'about' in the sentence and be correct.