Am I correct in thinking that he is definitely reading in someone else's room? If he were reading in his own room, wouldn't it read, "Он читает в своей комнате?"
I think so but in this special case you would literally say:
He is reading in her own room, which is a funny thing if you think about it.
How come this construction differs (seemingly to me) so much from the one about the baggage: "багаж у меня в комнате"?
он читает у неё в комнате=он читает в её комнате, same for yours. У неё=at hers literally (chez elle if you know French a little).
They're just different ways to say it. My Russian friend tells me "у меня в комнате" feels quicker to say so he naturally uses that, even though both forms mean the same thing. I suppose it could be that "в её комнате" could similarly just feel easier to say for some people. Not entirely sure, obviously.
Although in the "select a picture" exercise, the word "комната" shows a bed, hence, presumably, a "bedroom".