Can 'apartment' not stand alone here?
Not really; when referring to ancient Roman residences, an insula is specifically a type of building. https://en.m.wikipedia.org/wiki/Insula_(building)
"the dining room is in the appartment block" should be accepted.
It is also an island as I have seen elsewhere. I was surprised to see it here in this context after seeing it used in the other.
I think it's a bit idiomatic. It's still used this way in French and Italian sometimes.
A very common phrase in British English for the American "apartment building" is "block of flats" – Duo needs to accept that as a valid translation!
But how can a flat have an upper dining room, when they are flat?