What an interesting question! As we answer it, I think we'll see that the story is universal: that it could happen anywhere, during any time, because it's simply the story of someone so greedy and immoral that he succumbs to temptation and ultimately has to pay a hefty price for it.
As such, the tale deals with the heights of human greed and the destruction it brings, which is true no matter what time period or location we're in.
For example, let's move the story from early America to Elizabethan England. A penniless actor could meet the devil while out for a walk late at night, accept the devil's offer of riches, and quickly become a wealthy owner of many theaters, overcharging his audience members and forcing his actors to work long hours. Then one day as he's yelling at a group of actors, telling them that they'll have to take a pay cut and go hungry, he says, "The devil take me if I ever made a shilling off any of you!” At that point the devil could show up and take his soul.
See? It’s easy (and kind of fun) to imagine the story with a different setting.
Let’s do it once more: we’ll move it to the distant future, to a colony on Mars. A jobless Mars-dweller meets the devil while out for a spin in her hover-car. She accepts the devil’s offer of power and money and starts a terraforming company, charging exorbitant fees to colonies on other planets whose inhabitants need safer air to breathe. One day as she’s threatening to cut off a whole planet’s oxygen supply for failing to pay the ever-increasing maintenance fees, the devil swoops in and takes her soul.
Of course, you could write a more imaginative and elaborate version of the story if you like. The point is that the setting of “The Devil and Tom Walker” is interesting and adds color to the story, but it would work just as easily in any other time or place simply because the theme is universal.