"Whose room is this?"
I did the same thing. I believe the issue is in which term is the subject and which is the object. In our answer we have the room or 'this' as the subject, whereas the correct answer has the 'whose' as the subject.
間 (ㄐㄧㄢ/Jiān) would be a better measure word for 房間 but 個 (ㄍㄜ·/Ge) is also fine
There can be many nuances of meaning to the question here depending on how one says it. Sentence structure ("subject-object") has nothing to do with the correct translation. 这房间是谁的 ? - (curious) Whose room is this? "This room is whose?" does not sound natural in this case (except if somebody already told you whose room it is and you weren't listening). 这房间是谁的 ? - (disgust) Okay, whose room is this? (It's probably a mess.) 这是谁的 房间 ? - (shocked/incredulous/other appropriate emotion) This is WHOSE room? (Perhaps followed by: What do you mean it's his/her room? You mean, you gave this room to that---/insert expletive here/) 这是谁的 房间 啊? - (emotional) Whose room IS this? It's amazing/filthy/insert other appropriate adj./