"Strange! Why is nobody home?"
Consider which is the subject (hidden or explicit), and where it should be in the sentence.
I guess in the suggested answer 没有人 (= "nobody") is the subject, 在 the verb and 家 the object. I first thought 没有人 could be interpreted as 没有 (negated verb) + 人 (object) and 在家 would take the role of the subject, but I suppose 在家 cannot be used like that and I'd have to rephrase it as 为什么家里没有人.
Yeah! Remarkable. You have just answered yourself.
However it is not wrong to think of 没有人 as a negative form. If you say "(There) is someone at (my) home" you would say 有人在家; the negative form is naturally 没有人在家.