Roger's authority is simple, unadulterated force. No longer is his arm guided by a civilization that doesn't care about him-he is free to destroy as he pleases. And it certainly does please him to hurt. Roger is a sadist in the purest form, one who delights in torturing and causing pain. In fact, just before this particular moment, Roger has committed the first intentional murder on the island. He has cheerfully dropped a rock on Piggy, killing him and shattering the conch.
There is no power left on the island apart from this brutal force. With the conch gone, Ralph cannot even pretend to hold any kind of authority. Jack is now nominally in charge, but it is Roger who carries the true strength. As he advances on the twins, it foreshadows the new regime on the island. Of course, this idea will return when the twins tell Ralph that Roger has "sharpened a stick at both ends." He has returned to his original tactic of torture, seen in the first killing of a pig. This primal, savage streak is what drives Roger, & it is his faceless, nameless authority.