"The Diamond as Big as the Ritz" is good old social satire. By exaggerating certain aspects of American culture – the obsession with wealth in particular – Fitzgerald holds his society up to ridicule. By creating a parable to the expansion of the United States across the continent, he also mocks American motives behind and methods for success. The Washingtons, for example, are supposed to be descended from George Washington and Lord Baltimore – two leaders in early American history. Washington's willingness to manipulate and hurt others for his own financial gain is then a dig at the country's own tendency to do the same in its early expansion. (Braddock's slaves are a particularly potent example).
We're also looking at a coming-of-age story, though to a lesser degree. John is sixteen when the story begins and leaving home for the first time. In the course of the narrative, he learns a few lessons (maybe), experiences his first love, and all around grows up.
Lastly, "The Diamond as Big as the Ritz" is considered one of Fitzgerald's fantasy stories, mostly because, as far as we know, the existence of a giant diamond mountain in the middle of uncharted, secret territory in the center of Montana is the workings of an imaginative mind.