Most religions and philosophies have some sort of prohibition against desire or greed. Buddhists believe that suffering arises from desire. This includes not only physical desire but also ideas and thoughts. Christianity has warnings against pride and coveting. Taoism suggests a path of simplicity where desire is kept in moderation.
Allowing yourself to give over to desire can lead to a great deal of trouble, especially in a highly competitive culture like the United States. The desire to win or triumph can be highly addictive. This need to come out on top can lead to anger, ego, disdain, and a plethora of other negative emotions. It becomes difficult though to let this go.
Sports are never going away. Neither are beauty contests, country fairs, or simple board games. I think the key comes from not setting your worldview and self worth on the win or lose. Being secure in your path and your nature, the desire to win become less a need and more of a challenge to do better than yourself. Also, understanding the emotions that are attached to this desire to win is key. Knowing when the base side of instinct kicks in and acting as a soul seeking enlightenment reduces friction.