"After the debacle in Russia I left the country, for it was imprudent for an officer of the Czar to stay there. Many noble Russians lost everything. I, luckily, had invested heavily in American securities, so I shall never have to open a tearoom in Monte Carlo or drive a taxi in Paris. Naturally, I continued to hunt--grizzlies in your Rockies, crocodiles in the Ganges, rhinoceroses in East Africa."
There are several clues for modern readers as to when "The Most Dangerous Game" is set. First, it cannot be set later than 1923 since it was published in 1924 and is not of the futuristic science fiction genre. The second clue is that, when Ivan brings Rainsford some of the General's evening clothes to wear, Rainsford notes that the tailor was "a London tailor who ordinarily cut and sewed for none below the rank of duke." Thus the time period is one in which Russian Cossack nobles who are also generals traveled freely to England and shopped freely at exclusive London tailors. Thus the time period of the setting must be after Peter the Great and before--or only just after the Russian Revolution--a time at which Russian Communism reduced the privileged life of the noble to a level at or near the life of the Russian proletariat. The quote above provides the third clue while confirming and narrowing the deductions already made from the second. The "debacle in Russia" refers to the Russian Revolution of 1917. Thus the time period of the story is the five or six years between 1917 or 1918 and 1923.
As the General explained, he had invested his money in America (and so would never be reduced to working for a living because of need to "open a tearoom in Monte Carlo or drive a taxi in Paris" like so many exiled Russian nobles after 1917) thus could keep up elegant pre-1917 Communist Revolution elegance and luxury, a sampling of which Rainsford was treated to upon his arrival at the safe harbor (or so he thought) of General Zaroff's island. It is important to note that, in the pre-1917 world of privilege and elegance for Russian nobility, Zaroff had developed his taste for analytical applications of reason to hunting to a well-honed finesse (to a keen perfection) and had hunted everywhere and everything, including the savage African Cape Buffalo, which had hospitalized him and incapacitated him with a cracked skull for six months, and the "cunning" Amazonian jaguar, which he easily outsmarted. In fact, it is the jaguar hunt that led to the epiphany that he was beginning to be bored with hunting, a devastating realization for a man who has devoted his life to the hunt, as he said: "I live for danger, Mr. Rainsford." It was this epiphany, following this disappointing jaguar hunt, that led Zaroff to decide to assert his supremacy (doubtless a skill learned from a life of pampered luxury) to invent "a new sensation":
"It came to me as an inspiration what I must do," the general went on.
"And that was?"
The general smiled the quiet smile of one who has faced an obstacle and surmounted it with success. "I had to invent a new animal to hunt," he said.
"A new animal? You're joking."
"Not at all," said the general. "I never joke about hunting. I needed a new animal. I found one."