Kriegspiel, published in 1824, is believed to have been designed by a Prussian lieutenant named von Reisswitz.
More About Kriegspiel:
Originally played on a map of the French-Belgian border area, Kriegspiel became an obsession in the Prussian army, where game sets were sent to every regiment. It was extremely complex, but was (deservedly or not) credited with helping the Purssian army achieve military victories and so the craze for the game spread to other countries as well.
By the time Germany was defeated in World War I, it was apparent that the game's strategies did not always translate well to real wars.
Why Kriegspiel is Part of the Games Timeline:
Kriegspiel was the first attempt to create a realistic wargame, not the abstraction found in games like Chess. Here are the other games I believe are the most culturally and historically significant games published since 1800.