In my opinion, the story of the old men and their bowling is meant to help give the story its fake serious tone. This passage sort of refers us back to the beginning of the story and supplements the mock seriousness that we see there.
At the beginning of the story, Irving spends a lot of time telling us how this is a true story and that we can trust it because it was told by this old Dutch man. Here, at the end, we are once again told that the story must be true because it is in conformity with this old story.
I think that the men are also important because they lend to the atmosphere of romanticism in this story. We are also told at the start of the story that the Catskills are a very mysterious place where strange things happen.
So this little passage is meant add to the conceit that this is a true story and it is meant to add to the romantic tone of the story.
Washington Irving's "Rip van Winkle" shares some of the common narrative elements, or motifs, of folk tales such as the mysterious beings, and a potion that induces the enchanted slumber.
When Rip van Winkle wanders off on "his long ramble of the kind on a fine autumnal day," he finds himself on one of the highest parts of the Kaatskill (now Catskill) Mountains. The sound of "rolling peals like distant thunder" and the noise of balls which roll and echo like this thunder represent the sound of gunfire and the cannon balls being fired during the American Revolution.
It is typical of Rip van Winkle that he would not want to recognize a battle for what it is since he, then, might have to become involved. The men around him are perceived as small, perhaps, because they are, then, not worthy of van Winkle's serious attention. And, in his effort to escape any serious thought, van Winkle eagerly takes draft after draft from the flagon of liquor. And, when he awakens, he blames the "wicked flagon."
What is so humorous about the "scrupulous accuracy" of Irving's repetition of Diedrich Knickerbocker's tale is the whimsical irony put into it. For, Rip van Winkle chooses to ignore the approaching Revolution in his mind which represents the Romantic penchant of Irving, who indicates in van Winkle's return his nostalgia for the pre-revolutionary days of the past.