The story is set somewhere in the United States in a Pullman coach car.
Leacock himself was a Canadian writer, and his works were popular in the early part of the 20th century.
In the story, two men are conversing in a Pullman coach. Neither of the men recognize each other. However, each pretends otherwise. The text tells us that one of the men is wearing a "long fur-lined coat" and that he's carrying a fifty dollar suitcase.
Now, for a little bit of history. George Pullman built the first luxury coach cars in 1863. They were so popular that he commissioned more luxury cars to be built in 1868. These new cars were literally hotels on wheels. They were luxury accommodations and came complete with kitchens and dining rooms. Pullman coaches were usually reserved for private hire and were tethered to commercial passenger trains. Many of the hotels on wheels were leased by wealthy guests. For more about the history of Pullman luxury coaches, please refer to the links below.
Now, back to the text. Based on the history of Pullman coaches, we can make a few deductions. First, the man with the fur-lined coat and fifty dollar suitcase is presumably a well-to-do coach patron. As for timeline, Leacock likely wrote this story in the early 20th century. According to the CPI (consumer price index) calculator at the BLS (Bureau of Labor Statistics) website, $50 in 1913 translates to about $1,285.74 in July 2018. Note that the time limits for the calculator are January 1913 to July 2018.
So, we can infer that a man who could afford a $50 suitcase in Leacock's time (valued at $1,285.74 today) and a fur-lined coat likely had quite a bit of disposable income.
By all accounts, the setting for the story is a luxury Pullman coach in the early 20th century.