> I read in a history book that human beings managed to coordinate entire empires that stretched across continents with out digital electronics.

You asked specifically for little leagues. The across continents coordination is done by a.) delegating rulership to local warlords b.) keeping military power strong enough to keep those you those in check. It had massive limitation in terms of what it could achieve and has zero to do with organizing of competitions for kids.

Plus, the central power would not bother to micromanage little teams. It is our culture that finds little leagues important, not theirs.