I think if he had shot his family while being intoxicated he would not have looked as he did in his mugshot. He would have been looking either still drunk, or hung over and shocked and remorseful (depending on how soon after the arrest the photo was taken). But he looks sober and okay, as if he has no worries, as if his family did not just die in a horrific shooting at home, and by his own hands.
No I don't think this was loss of temper control due to alcohol. Either he simply lost his temper because that's what he does habitually, or he even planned the whole thing. He looks too relaxed, almost satisfied as someone pointed out above.
ETA: how strict is his religious code, I wonder? Was the fact that his stepdaughter and her boyfriend were living together in his house unmarried a source of grievance for him?