This is a powerful question. I think it goes right to the heart of all literature. I would say that the American Dream as depicted by Fitzgerald is one that does have relevance to the modern setting. One of Fitzgerald's strongest arguments is that Gatsby's dream, and the American Dream of the 1920s, lacked any potential for lasting happiness because it was constructed on a firmament of selfishness and self- interest. There is little to indicate that the flapper society of Tom, Daisy, and Jordan has any connection to the well-being of others or any socially or politically redemptive notions of the good. In this light, Fitzgerald is implying that for others to find some lasting vision of happiness, they have to broaden their understanding to include others. The reader assesses that the lives of the characters in the novel will all be impacted by the Great Depression and the economic challenges of the 1930s that will undercut all of these individuals' pursuits. In the end, their dreams will be nothing more than vestiges washed away by the tide.
Where this is relevant to the modern reader is in its paralells to today's settting. The battle for where the line is between material acquisition and long term happiness and what constitutes the latter is still debated. Given the current economic crisis that is impacting so many, the issues brought out in Fitzgerald's depiction of the American Dream are relevant. We still see the same questions of what it means to be happy, and how material wealth can be compatible, while expanding our social and political frames of reference, relevant to our modern condition. At the same time, individuals in the modern setting can see the relevance of a Tom or Jordan, who use people as means to an end, or a George Wilson, who struggles to be heard. In this light, the pursuit of the American Dream as shown in Fitzgerald's work is about voice, something that is applicable as much now as it was then.