It was a prize he had desired as a young boy, and he owed it to that young boy to achieve the feat regardless of whether he still wanted it.
Gatsby needed to strive towards some goal or else he would feel empty. If he did not have one clear goal in mind he would feel completely empty. Daisy did love Gatsby, but she also had loved Tom for a time. She knows that she will never be able to deny that fact, but Gatsby wants more than just Daisy's love now, because his quest is to have her denounce everything other than her love for him, something he know she can not do. But he does not want Daisy because he loves her, he wants her for the sense of accomplishment.