Third Person Omniscient
The narrator here is wholly omniscient, meaning that the narrator can let us in on any character's inner thoughts at will. However, we get most of the story filtered through the point of view of our various main characters—including Roark, Wynand, Keating, Dominique, and Toohey—with occasional cameo narrative stints from people like Katie Halsey.
The points-of-view go like a revolving door, altering out by chapter, and sometimes within chapters. And the third person omniscient narrator keeps the narrative moving, shifting the spotlight to focus on different characters. The narrator tends to stay in the background and lets the characters themselves dictate the story.
However, that doesn't mean the narrator is totally objective and that the characters aren't in cahoots with the narrator. All the characters here act as philosophical mouthpieces and either express views that the narrator (basically Rand herself) agrees with or views that she sets out to prove as "wrong." For example, check out this quote:
The public asked for crime, scandal and sentiment. Gail Wynand provided it. (3.1.170)
This is not an unbiased narrator commenting on either Wynand or society at large. This quote is almost glowing with Objectivist sentiment: society is dumb, and Gail Wynand is a baddie for providing trash to appeal to the masses.