Anton does not kill at random or without purpose. Anton sees himself as a hand of fate. Anton Chigurh is an emotionless, compassionless killing machine and is now one of the most iconic villains of all time. He carries a silenced assault shotgun and a cattlegun aka a captive bolt pistol, which fires a cylinder from a hose which is connected to a tank of compressed air. In this scene Anton uses the CBP on a stranger just for his car.
If you look closely you'll notice a mist of blood coming from the front of his head, not the back because there's no exit wound. In the film Tommy Lee Jones' character explains how the bolt only goes far enough in to kill.
A lot of interpetations on this film, one even goes to say that Anton Chigurh is really Ed Tom Bell performing the actions he cannot do within the limits as sheriff. That he uses this fake personality to remove a cynical narcotics cartel from his district, and has to kill everyone that can expose his murderous actions. A little far fetched, but interesting.
There has been much discussion about the fate of Moss, the scene involving Bell and Chigurh ,and more. Click on the respective links for the REAL answers.