This is nonfiction, so the question of the narrative technique doesn't play the kind of role that it would in a novel about, say, a boy named Harry (hero!) meeting an old fogey named Dumbledore (mentor!).
Instead of getting the story of Harry Potter, we're getting a book that breaks down Harry Potter (and basically every other book) into bite-sized analytical pieces.
Campbell writes the same way he might give a lecture in a university: making his point and then backing it up with examples as evidence. We definitely jump around as needed—mostly from one myth or story to the other—and that serves the same basic purpose as third-person omniscient narrative (getting us the info we need to understand what's going on).
But it's not a formal narrative, just an analysis of a narrative, so we can hear it all coming from just one guy and his (pretty crazy-genius) point of view.