You'll also recall that Herod ordered the death of all boys under 2 when Jesus was born.
Are you going to say that these Murders of the Innocents by "the properly constituted government" is not murder?
My point is that the acts you refer to are not those I'm talking about, and there is a difference. I'm talking about everyday murder. Suppose you and I are neighbors and one day I get it into my head to go over to your home and slit your throat. My action would not have been tolerated in ancient Egypt, or Palestine, or feudal Japan, or China. It wouldn't have been tolerated by the Aztecs or the Incas. It would not have been acceptable to Eskimos or the aborigines of Australia or the Maoris of New Zealand.
The reason it would not be tolerated is because it is a dead end activity. It leads nowhere. Just as the path that begins with 2+2=5 ends nowhere, so does the path where any member can murder any other member. It is such a monstrously stupid idea, it is never even tried.
You speak of actions of a ruler/leader on behalf of the society. Those are different. Judges can't be held accountable for decisions they make in the capacity as judge. Not even for bad decisions or wrong decisions. They can be held accountable for theft or mayhem they do as an individual. They can be held accountable when they misbehave as a juddge. So, if Herod was acting as an individual and not a ruler, it would be murder. If Herod was misbehaving as ruler, that is overstepping his authority, he would be a murderer. If the structure of the society were such that his authority were absolute, well, that would be hard to overstep.
By the way, do you believe Ted Bundy was murdered? If Martha Stewart is found to have profited illegally from insider trading and her punishment includes a fine, would you consider that theft?