This is a good observation. I just rechecked the story and only at the midpoint of the story does it come to Rainsford's attention that General Zaroff was hunting humans, and in my version it's only on page 11 of 15 that the General reveals to Rainsford that Rainsford himself will be the hunted. So, your observation is correct. There is a delay in introducing the main conflict.
The main reason for this is Connell wants to build suspense. He is masterful in doing so.
In the beginning, Rainsford is on a boat in an exotic location. In fact, it is revealed that the island yonder is called Ship-Trap Island. Hence, danger is in the air. Cannibalism is also mentioned. As he is talking with his friend, Rainsford also says that there are only two types of people in the world. He says: "The world is made up of two classes--the hunters and the huntees." Little does he know that he would live these words.
As he finally makes it to the island, the setting and his initial interaction with Zaroff adds to the setting of fear. No matter how kind and charming Zaroff is, there is something very ominous. Here is first impression:
Rainsford's first impression was that the man was singularly handsome; his second was that there was an original, almost bizarre quality about the general's face. He was a tall man past middle age, for his hair was a vivid white; but his thick eyebrows and pointed military mustache were as black as the night from which Rainsford had come. His eyes, too, were black and very bright. He had high cheekbones, a sharpcut nose, a spare, dark face--the face of a man used to giving orders, the face of an aristocrat. Turning to the giant in uniform, the general made a sign. The giant put away his pistol, saluted, withdrew.
As Rainsford and Zaroff talk more, it becomes apparent that Zaroff is a mad man. It is clinched, when Zaroff wants to hunt Rainsford, simply because he is bored. Hence, suspense is built until the climax.