I would think it is because General Zaroff is trying to size Rainsford up, to see what he is "made of" and to try to predict how his coming will affect Zaroff's life and hobby on the island.

Zaroff has been here on the island with no other people that he would see as his equals.  Now here comes Sanger Rainsford who is a great big game hunter just as Zaroff thinks of himself.  This would naturally make Zaroff curious.

He will wonder how Rainsford's presence will change things.  Will Rainsford join him in the hunt?  Will they compete with one another to see who will be the better hunter?  Will (as it turns out) Rainsford be repulsed by the idea.  If so, will Zaroff be able to successfully hunt him?

All of these questions must be going through Zaroff's mind and this is why he studies Rainsford.