Why doesn't the narrator reveal the main conflict until a great deal of the story has passed?
You are correct in stating that the main external conflict doesn't begin until the story is about halfway done. That main external conflict is Rainsford's fight for survival against Zaroff. I think the author's intent is to allow plenty of time for indirect characterization of Rainsford. Readers know that Rainsford is a hunter at the beginning of the story, but we don't know exactly how good of a hunter he is. By putting off Rainsford's battle with Zaroff, the author is able to include small details about Rainsford's experience as a hunter. For example, Rainsford is able to distinguish that the shots he heard in the distance were from a small caliber pistol. His thoughts are confirmed when he finds a shell casing from a .22 caliber pistol.
Also, by placing the main conflict late in the story, the author is able to really show readers how Rainsford feels about hunting. He sees no problem with hunting down prey. That's why he chides Whitney for even suggesting that they feel some sympathy for the jaguars. Rainsford is also excited by his early conversations with Zaroff. He sees Zaroff as a fellow experienced big game hunter. All of those things help highlight the shift that occurs in Rainsford once he becomes the prey. Rainsford stated that he believed that hunting another human is murder, so what will Rainsford do once he is the prey? If Rainsford goes on the offensive, then he isn't really doing anything differently than Zaroff is. Rainsford's plight is made more interesting by placing it late in the story because readers have so much evidence to the fact that Rainsford just might not try to kill Zaroff.
In my opinion, the author does this because he wants to show us something about Rainsford's personality and his beliefs. I think he does this because the story is partly about how Rainsford's experiences affect (or do not affect) his beliefs.
By having the main conflict start so late, the author is able to show us more about what Rainsford is like before he gets hunted. We see, for example, that he has no sympathy for the animals he has hunted. But we also see that he thinks that the idea of hunting people is totally abhorrent. Because we get this detailed view of his opinions, the rest of the story becomes more interesting. It especially makes us very curious as to what the ending implies. What will Rainsford do now that he has killed Zaroff -- will he stick to his values or will he do what Zaroff had been doing?