At håbe is a transitive verb, meaning it must always take an object. So you cannot say just de håber (missing object); instead you can say either:
- Det håber de where the emphasis on what they're hoping for, sort of like the so in English: Er han i live? (Is he alive?) --- Det håber de (they hope so).
- De håber det which is still they hope so but with a larger emphasis on who's hoping. This construction is seen more often with a clause replacing det such as de håber at han er i live meaning they hope that he is alive.
Since de is the third person subject pronoun, it cannot be translated to them (which is an object pronoun, dem in Danish). It is always the subject (they). The word order is therefore rather free in this particular sentence, which is maybe what's confusing you :)
Indeed, and also to Dutch «Dat hopen zij». Det/Das/Dat is the object of the sentence. In English, to have a construction with the object as the first word, you could say «That is what they are hoping for». Quite long, hence the change in word order compared to Danish/German/Dutch.