Not sure why you consider the Word Reference translation doesn’t make sense but there is no way to understand désœuvrés differently.

The police officer is just telling the parents are jobless and bored.

Meaning B-. in the TLFi: Personne atteinte d’ennui, de lassitude.

I don’t agree with jlliagre’s interpretation of the definition for désœuvré.

In these two links, we can find the following definitions:

Qui est mal à l’aise, désemparé, prostré parce que soudain privé de son centre d’intérêt.

Qui n’a rien à faire, qui n’a plus d’activité essentielle ; privé de son centre d’intérêt.

In this context, the parents are not only "bored" and "jobless", they feel like everything is pointless because they have been deprived from their center of interest, which is their son (who was recruited in Daesh and therefore probably left the house).

I believe the terms idle, aimless and shiftless can all convey the meaning of désœuvré.