Certainly, in Part I of the story, the point of view is third person omniscient. The narrator is not a participant in the events (and does not use the first person pronoun "I"), but he or she can and does report on how all characters are thinking and feeling: Paul, his teachers, the principal, the people in the audience at Carnegie Hall. In Part II, we learn quickly, for example, that Paul "felt grimy and uncomfortable" from his train ride. His perceptions, thoughts, and feelings seem to dominate this section of the text. We soon realize that the narrator of this second part is third person limited omniscient, as we only get Paul's thoughts and feelings, as opposed to everyone's around him. This makes good sense, given the content—Paul does not care how anyone else thinks or feels; he only wants to focus on himself and on living his best, fullest life. After he steals the money to fund a short-lived though lavish lifestyle in the city, he felt that "Everything was quite perfect; he was exactly the kind of boy he had always wanted to be." Without other people,
He was not in the least abashed or lonely. He had no especial desire to meet or to know any[one]; all he demanded was the right to look on and conjecture, to watch the pageant. The mere stage properties were all he contended for. Nor was he lonely later in the evening, in his loge at the Metropolitan. He was now entirely rid of his nervous misgivings, of his forced aggressiveness, of the imperative desire to show himself different from his surroundings. He felt now that his surroundings explained him.
Paul is most comfortable with himself now and feels no need to explain or dissemble or even speak to others. Therefore, the narrator provides no other characters thoughts or feelings because they are of no importance to Paul at this point.