Okay, there are a few stories about old games that would be played, ranging from hide-and-seek to running along a plank (that was gradually raised in angle) for Shoten no Jutsu, methods of running that encouraged endurance, games of dodging objects, and more. Realistically, that's all they were, games. But it may be noted that pretty much all sports that exist are extensions of older forms of warrior training, team sport is pretty much the modern equivalent of inter-village warfare (which goes a long way to explain the way supporters react, soccer riots etc). Even to the point of games like Chess being based in military strategy (my favourite story about the possible origin of Chess is that it was devised by a Middle Eastern prince to explain to his mother, though symbolic military strategy, exactly why he had to kill his brother).
