This quote comes from General Zaroff, who explains to Rainsford that hunting animals has lost its thrill for him. Since he is a consummate hunter, he believes his whole purpose is to pit his wits against a worthy prey; unfortunately, animals cannot think past a certain intelligence level and so Zaroff has become far too cunning and knowledgeable about their habits to be excited by hunting anymore:
"No animal had a chance with me any more. That is no boast; it is a mathematical certainty. The animal had nothing but his legs and his instinct. Instinct is no match for reason. When I thought of this it was a tragic moment for me, I can tell you."
(Connell, "The Most Dangerous Game," classicreader.com)
Zaroff goes on to prove his superiority by predicting or escaping all of Rainsford's traps; in fact, after tracking Rainsford down he deliberately refuses to take a shot and leaves, allowing the hunt to continue. For the whole hunt, it seems that despite Rainsford's equally powerful hunting skills, Zaroff will win. At the end, however, the quote is disproved; Rainsford instinctively leaps off a cliff to avoid being killed, and is able to return to Zaroff's chateau for a final battle.