The authorities are precisely the proper people to turn the "child" over to. Only they would have the resources and skills required to determine whether the troll has performed similar acts before and whether he is a psychotic (of course the parents also likely know, but aren't likely to do anything effective).

Also because it provides a record of his activity for future reference.

I don't believe the "game" excuse - I think the troll is a full-blown psychopath.