If we want to approach The Great Gatsby as a love story, we have to look at the innocent beginnings to the love between Daisy and Gatsby. As in so many great love stories, there is a moment of pure, innocent affection shared by the two.
This affection is tied up in the vision that each character has for his/her future. These visions are challenged by the intervention of circumstance - another trope of the classic love story. The obstacles in the way of a successful relationship persist even to the end of the novel, as Daisy and Gatsby never get married.
In this way, Gatsby is not the quintessential love story. The lovers fail. Even in tragic love stories there is some success for the lovers, some unbreakable bond established. This is not true for Gatsby.
I think that Fitzgerald's work might be the quintessential Romantic story. I don't see it as the most representative of a love story because I don't think that Gatsby loved Daisy. I think that he was in love with the idea of being "in love" with Daisy. Part of what makes the story so powerful is that Fitzgerald is able to reveal the social inauthenticity as reflected in the characters. This is why Gatsby's attempts to redefine his own sense of self and his pursuit of Daisy are doomed to failure for he is a representative of the time period that is materialistic and shallow, with little in way of real and transcendent values. When one's consciousness is imbued with only the temporal, there can be little room for something as universal and as permanent as love. It is for this reason that Gatsby's narrative is one that represents the quintessential story about the love of being in love. There is little in Gatsby's exploration that represents true love, something that he would concede in the end because his entire vision of "winning" Daisy over and being the man he wishes to be in his own mind both fly in the face of the honest and open sacrifice of what it means to be in love. It is in this realm where I think that he is more of a Romantic and probably a quintessential one at that than anything else.