Dexter dreams of not only beating the men at golf in marvelous fashion, but he also dreams of living their glamorous lifestyles and experiencing their almost worshipful admiration of him (similar to his own admiring perspective of their lives and fame).
Fitzgerald includes this description at the beginning of the story when Dexter bemoans winter's effects on the fairway, and so instead, in his mind,
"he became a gold champion and defeated Mr. T.A. Hendrick . . . [or he steps] from a Pierce-Arrow automobile . . . [or he strolls] frigidly into the lounge of the Sherry Island Golf Club"
as he is surrounded by admirers or gawked at by Mr. Mortimer Jones (another golfer). Dexter's dreams about what life would be like as the idle Old Money golfers demonstrate that possessing a lot of money is not his objective; rather, he wants the fame, superiority, and seemingly effortless effect that belong to the men for whom he caddies.