It might be. Does a killer always have to be a psychopath? Again, hey, he might be a raving psychopath and, under neurological examination he may be found to be fitting the medical diagnosis. And I like the work of Bob Hare and subsequent research that has examined the field, such as Hoffman, but they have created a convenient monster.
It's said 1% of the general population is a 'psychopath' - that's about 30 million people worldwide in 1985, so there's a chance he is, particularly given that he killed his entire family and the general population of jails house between 15%-25% of all inmates being labelled psychopaths. The odds are not in his favour, I grant you. He scores highly on the Hare checklist and the PCL-R. But it's not definitive because we still haven't seen these tests ever having been conducted, as a minimum.
Define "killer". If you're a purist who believes that all taking of another's life is murder, then No, NOT all killers are psychopaths. If, however, the taking of another's life is done, without showing regard for that life, for gain, be it financial, sexual, or position, and the murderer presents their rational justification for it, I'd say they were a psychopath.