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.