Roger is the "hangman" because he is sadistic and probably would be considered a sociopath. Roger quickly loses any sense of civility that he might have had. In chapter 4, Roger throws stones at Henry who is in the water, but he doesn't hit him; he hits all around Henry because "Roger's arm was conditioned by a civilization that knew nothing of him and was in ruins." Roger wants to hit Henry, but he has been conditioned by rules NOT to hit him. He quickly loses any sense of restraint brought on by the rules though and by chapter 11, he is fully and gleefully savage when he releases the rock onto Piggy, crushing him. In the previous chapter, chapter 10, Roger is told by Robert that one of the littluns is scheduled to be beaten for no apparent reason and Roger nods that this a good turn of events. The narration tells us he "...sat still, assimilating the possibilities of irresponsible authority." Roger epitomizes the evil that Golding felt each person had within him. He has no moral consciousness telling him he shouldn't commit immoral acts. If allowed to continue on the island, he would probably have taken over command from Jack eventually. Jack had a reason for his actions, even if it wasn't a good reason - he wanted control and power. Everything he did was designed to help him achieve that goal. Roger's only goal was to satisfy his own bloodlust. He is, with little doubt, the scariest person on the island.
Roger is gradually built up as an ominous figure. Initially, throwing stones "to miss" at the littluns, Roger has the potential for violence, but his hand stops. It "was conditioned by a civilization that knew nothing of him and was in ruins". Those stones, of course, become the stone which kills Piggy, and Golding builds up, stone by stone:
Silence and pause; but in the silence a curious air-noise, close by Ralph’s head. He gave it half his attention—and there it was again; a faint “Zup!” Someone was throwing stones: Roger was dropping them, his one hand still on the lever.
Then, there is, a further build up to the moment where Roger, pointed up by Golding as enjoying it, leans on the lever which tips the massive rock down onto Piggy:
The storm of sound beat at them, an incantation of hatred. High overhead, Roger, with a sense of delirious abandonment, leaned all his weight on the lever.
Public stoning, in the Bible, was a punishment meted out to adulterers and people in social disgrace. Roger has become the public executioner of all that stands against Jack's cause: "See!" Jack shouts "That's what you'll get".
Yet Jack recognises that Roger's deed, killing Piggy, has given him an ominous untold power. When he comes down from the rock...
The chief spoke to him angrily.
“Why aren’t you on watch?”
Roger looked at him gravely.
“I just came down—”
The hangman’s horror clung round him. The chief said no more to him...
No-one can speak to him. He is a murderer: he is more ominous, more powerful, even than Jack. And it is Roger, at the end of the chapter, whose presence becomes the frightening one when Samneric do not want to join Jack's tribe:
Roger edged past the chief, only just avoiding pushing him with his shoulder. The yelling ceased, and Samneric lay looking up in quiet terror. Roger advanced upon them as one wielding a nameless authority.