Basically, Zaroff gets people to play the game by forcing them to do it. He makes it so that playing is the best option that the people have.
So how could this be? How could your best option be to run off and try to hide while some guy comes to hunt you and kill you if he catches you? Well, it is the best option if your other option is that you will die for sure and die for sure in a more painful way.
So what Zaroff tells them is that if they do not let him hunt them, he will give them to Ivan and Ivan will kill them in terrible ways. Here is the quote that shows this:
"Oh," said the general, "I give him his option, of course. He need not play that game if he doesn't wish to. If he does not wish to hunt, I turn him over to Ivan. Ivan once had the honor of serving as official knouter to the Great White Czar, and he has his own ideas of sport. Invariably, Mr. Rainsford, invariably they choose the hunt."