As a teenager, what daydream does Dexter Green have about the men he caddies for?

We'll find this answer in the fourth paragraph of the story:

"He became a golf champion and defeated Mr. T. A. Hedrick in a marvellous match played a hundred times over the fairways of his imagination, a match each detail of which he changed about untiringly--sometimes he won with almost laughable ease, sometimes he came up magnificently from behind. Again, stepping from a Pierce-Arrow automobile, like Mr. Mortimer Jones, he strolled frigidly into the lounge of the Sherry Island Golf Club-- or perhaps, surrounded by an admiring crowd, he gave an exhibition of fancy diving from the spring-board of the club raft. . . . Among those who watched him in open-mouthed wonder was Mr. Mortimer Jones."

As you can see, while Dexter is working as a caddy during his teen years, he imagines that he becomes a fantastic golf player himself. He fantasizes about beating Mr. Hedrick (one of the men Dexter caddies for) in lots of different ways: sometimes in a straightforward way, and sometimes in a slower, sneaky, more startling way. In his daydreams of success on the golf course, Dexter also gets out of a fancy car and walks inside the club building (like his boss Mr. Jones does in real life) and sometimes he does a skillful dive into the water while lots of people watch him admiringly.

Basically, Dexter daydreams about not just being one of the men caddies for, but being the most successful of them and the most admired among them.

Dexter's daydreams here indicate that he craves success, power, wealth, and the admiration of others. As the story continues and Dexter grows up, his basic desires don't change, but the specific ways in which he seeks to satisfy them do. For example, as a kid, Dexter wants to be admired as a golf champion. But as a young adult, Dexter wants to "win" Judy for himself; she's the new, grown-up version of a prize or trophy, in Dexter's mind. However, the one thing that stays the same is Dexter's desire for great wealth. He remains ambitious, surprising even himself with the financial success he eventually gains. But it doesn't make him happy.