Dexter has grown up around people with more money and higher social status than his family, who were grocers. The years that Dexter spent caddying at the golf club brought him into contact with people that he wanted to eventually surpass in success. As he becomes a young man, he decides "He wanted not association with glittering things and glittering people--he wanted the glittering things themselves."
While young men his age from wealthier families entered more precarious professions, including selling stocks and investing, Dexter became a practical-minded business owner and earned a fortune rather quickly. His ambition was not to befriend his social superiors; Dexter later plays golf with them and finds them limited, untalented, and boring.
Dexter himself doesn't fully understand why he pursues success and how he should be enjoying it. The narrator observes that "often he reached out for the best without knowing why he wanted it." Perhaps Dexter is caught up in the American consumerism that arose in the wake of WWI. It was easy for people to acquire more consumer goods and services during this time, and Dexter seems to have fallen into this collective enthusiasm for the things his success provides.