Why Are Rich People So Bad at Sports?

Because as sports became lucrative careers, as opposed to expensive hobbies, young hungry people applied themselves to the fullest in sports as their ticket to upward mobility.

Sports, in turn, lost their cachet and prestige (Prole-drift) and the rich went to find other activities with high barrier of entry, like golf, car collection, yachting, high-stakes gambling or even newer types of toy businesses (film, media, fashion, etc.) and finance to channel their competitive drives.

Why is Vanity Fair asking stupid questions they don't intend to answer?

An irrelevant example. Why didn't the author choose an example from a sport where the poor and middle class had reasonable access to facilities and training?

Perhaps the transition was another result of the gradual democratization of our culture. With more and more people able to participate in games that had previously been available only to the leisure class, the one percent just couldn’t compete.

This is a good guess, but here's another one: Perhaps William Larned was able to devote his life to tennis because he took his place in the upper class for granted and didn't feel like he needed to prove his worthiness. Perhaps the democratization of culture means that the rich now feel more pressure to prove or earn their right to be so privileged, so they put their energy into education and professional achievement.

Devoting oneself wholeheartedly to a sport means neglecting all the more reliable ways of maintaining one's status. In days past, most people who inherited a place in the upper class didn't feel particularly pressed to maintain it or prove they deserved it. They just assumed it was a fact of life. Enterprise and noblesse oblige were only for those who felt inclined to them. There was nothing to lose by devoting one's life to whatever one wanted, whether that was sport, adventure, or partying.