Not only does this sound right, sport was long seen as a way of training the young for war. Many games develop rules that highlight things like teamwork, sacrifice, etc.
My understanding as a Yank has been that the British in the heyday of the Empire saw sport as positive because it prepared the children of the elite to become officers -- Someone who knows --does that sound right?
Agreed Dave great points, in fact your insight tiggers the Spartans and their culture, and even the Samurai (??) to add to your list. Great minds like alike