Why might Chekhov have chosen to open the story in a party setting?

The banker is throwing an all-male party, a "stag party." This is significant because the men would not be talking about prisons and capital punishment if there were ladies present. The banker is too proud to call the bet off without the lawyer's assent. The banker made the bet in front of a large group of important men. He would be humiliated if he backed out. That is why he tries to talk the lawyer into calling it off.
"Think better of it, young man, while there is still time. To me two million is a trifle, but you are losing three or four of the best years of your life. I say three or four, because you won't stay longer. Don't forget either, you unhappy man, that voluntary confinement is a great deal harder to bear than compulsory. The thought that you have the right to step out in liberty at any moment will poison your whole existence in prison. I am sorry for you."
Chekhov knew he would have a hard time selling the reader on his story's premise. So he deals with the possible objections by having the banker himself acknowledge them.
And this wild, senseless bet was carried out!
"What was the object of that bet? What is the good of that man's losing fifteen years of his life and my throwing away two million? Can it prove that the death penalty is better or worse than imprisonment for life? No, no. It was all nonsensical and meaningless. On my part it was the caprice of a pampered man, and on his part simple greed for money ..."
By stating the reader's own objections, Chekhov shows his literary skill. He doesn't try to ignore the reader's doubts but meets them head on. Then when the solitary confinement actually begins, the reader is more likely to accept the bizarre terms and conditions as plausible.