I don't know about that. The $4,500 difference would have been a big deal in '38. Look at the article about PGA tour money winners at the bottom. $5,008 would have been good for 9th place or thereabouts. Sam Snead's $19,039 makes him the all-time richest golfer.
Maybe this article shows we have de-emphasized one sport in favor of another sport. Or maybe, society did not find sports as important back then since there wasn’t as many professional associations. Or maybe the population has grown so more consumers require more professional sports and the market dictates salary growth.