In "The Most Dangerous Game," General Zaroff is a man who purposely lures ships on to rocks so they can be shipwrecked. When the men from the ships get to his island, he uses them as prey for his hunts.
So, what's ironic here is that he's pretending to be very civilized at the same time that he's doing this stuff. He's got a butler, he talks with an aristocratic accent, he tries to act like he's very civilized. But that's ironic because what he's doing with his hunting is pretty much the opposite of what civilization stands for.
So the irony is that he acts (and wants others to act) in a civilized manner even as he is doing this totally barbaric thing.