Although the story is told in the third person, we see everything happen through Conor's eyes in A Monster Calls. Even when Conor and the monster are one, we're getting Conor's side of the story. For example, when Conor beats up Harry in the lunchroom, and the narrator says, "Then the monster leapt forward to make Harry see," (23.46) we know it's really Conor doing the leaping.
Why? Because nobody else sees the monster, as we learn at the beginning of the next chapter when the headmistress tells him, "I'm not even sure how one boy could have caused so much damage by himself" (24.8).
If this were written in the first person, though, that mystery would be solved, right quick. Conor would tell us straight up what's going down. Keeping the book in the third person keeps us at a proper distance, and allows us the ability to both experience the story along with Conor as well as to stay far enough away from his pain to give us some much needed perspective.