The translation to English is incredibly awkward. Accordingly cannot be used in this expression and make sense to a native English ear.

this phrase seems very, very odd to me. is it really something that a German would say? what does it mean?

I don't understand this either - we would never use such a phrase

I also thought it was something like "It seems appropriate in the apartment" since "in der Wohnung" is out of the "sehen ... aus" construct.

my problem - already mentioned by someone above - is with what i think is the sehen-aus, or rather aussehen construction here. If the principle verb here is indeed aussehen - a seperable verb - shouldn't aus go to the very end of the sentence? Also, what is the role of the preposition 'in' here? Following Menschenkind's explanation, I imagine the idea here being something like, 'It looks accordingly/as such in(side) the apartment.' Or perhaps - with all due respect for them - this phrase is simply a bit of a boo-boo on duolingo's behalf....

One would have to say "His apartment looks the same"