This is an interesting question for this story, because I have always thought that the story wouldn't be that much different if it was written in the first person perspective. While the narration of this story is third person, it is not third person omniscient. It is third person limited. The narration is almost exclusively focused on Connie. Readers know her thoughts, actions, and feelings, and we do not know much of that information about any other character. This makes Arnold Friend as mysterious and creepy to readers as he is to Connie. We feel her fear, and we have no idea what Friend is up to and about. All of that can be accomplished with a first person perspective, yet this story is told from the third person perspective. This allows the narrator to explore Connie's world in a little bit more depth than would be possible in first person. The opening paragraphs are a good example of this. They give readers information about Connie, her sister, and her mother. The third person narration allows the narrator to give information that is beyond Connie's limited teenage perspective.
Her mother, who noticed everything and knew everything and who hadn't much reason any longer to look at her own face, always scolded Connie about it. "Stop gawking at yourself."
The other thing that the third person perspective does is create a bit of distance. This limited perspective creates distance from other characters, but the third person perspective creates distance from Connie's narrow worldview. The point of view allows the story to be more of an allegorical/moral/symbolic story. First person narration would make the story a horrific account of a young girl's abduction. The third person perspective still tells that story; however, it also conveys an "and let this be a lesson to you" message. The story could be interepreted as a warning for young girls like Connie in all places.