Jack feels the urge to stalk and hunt so strongly that it is visceral, much like a hunger in his gut. It would be logical that by the process of projection, he would assume other people felt the same way as himself.
Remember also that the jungle is personified up to a point, beckoning the boys to explore its interior (and their "interior" as well!) This is no simple game of tag or hide-and-seek but is a true test of survival of the fittest. Jack, too, feels vulnerable as he pushes his skills to the limit.
(Remember that Jack is just a "virtual" character and not a real person who exists outside of whatever the writer shows. We cannot know more than what is stated or implied about him.)
Jack is being "hunted" by the beast within himself. It is creeping up on him, just like when you are sad and you are trying to keep it inside, but really it is there inside of you, something that you can't ignore. Jack can't ignore his savage and primitive side, and it is coming out as he continues to hunt and kill.
Jack feels as though he is being hunted down at times because he doesn't feel secure in his role as leader. He knows that he could never be the leader that Ralph truly is. Ralph's leadership is all about what is good for the group; Jack's leadership however is self centered. Jack is only interested in what is fun and what will make him seem more powerful. So while Jack has intimidated several of the boys on the island to follow him, he knows that the boys don't think of him as a true leader but just fear him and feel they have to follow him for their own safety.