"That is our room."
Translation:Das ist unser Raum.
Unserer is dative - as in "Wir spielen mit unserer Katze" but here there's no dative. Hence unser for singular neuter nouns.
In this case there is no difference. But "Zimmer" is only used when you mentioned the rooms in a flat or building. "Raum" you can also use for this but it can also be used as translation for "area", "sector" and "distance". For example "the distance between us" (der Raum/die Distanz zwischen uns), " at the policitcal sector of Hungary"(im politischen Raum von Ungarn), "in the area of London you find a lot of footbal fans"(im Raum London findet man viele Fußballfans).
Can someone explain why Unser and not Unseren? it is "Der Raum" after all.
After verbs like "to be", it is not accusative but nominative. It is an attribute, not an object. It is not something on what the subject do something, but it is equal to the subject. Here "Das" means, equals "unser Raum". And the form in nominative masculine is "unser".
Room can be also Platz ( There's no room for it. / Da ist kein Platz (da)für. ). Zimmer is adequate too, when the context is more like 'chamber'. Raum - Zimmer / room - chamber
I agree with the thinking that Raum and Zimmer are interchangeable in this case