Interesting: Long before Gary Gygax, or Avalon Hill, the first recreational war game was published by H. G. Wells in a book called Little Wars, which carried the wry subtitle: A game for boys from twelve years of age to one hundred and fifty and for that more intelligent sort of girl who likes boys' games and books.
Wry, for obvious reaons, and also ironic, as Wells was a pacifist whose game was meant to demonstrate that after "three or four" tries the game would reveal "what a blundering thing Great War must be" -- Great War apparently being an operative culture concept before the Great War, and perhaps a telling note of historical inevitability. Wells imagined that Little Wars could, well, make wars little; that simulated combat could replace the real kind. But of course military people loved Wells' system, with its strategic rules and toys and little projectiles, and the world was less than a year away from the First World War.
Here is an image of Wells and some other dapper gentleman on their knees, struggling against the tide of their un-gentle time:

Much later: Marxist philosopher and film-maker Guy Debord, he of the lasting titles, spent the last two decades of his life convinced that his legacy would actually be about a war game called Kriegspiel. (Like its namesake, but less one "s.") Kriegspiel is a board-based conflict game between generic opponents -- Northern Territory and Souther Territory -- that, in DeBord's worlds is meant to encapsulate "the dialectic of all conflict."
It looks like this:

Apparently, the game is dense and difficult to play and never caught on, and there were only a few copies made with the nifty metal pieces. Recently, it was adapted into software but has attracted few players. That hasn't stopped these guys from making a weird, but compelling conceptual film based on Kriegspiel, called Class Wargames:
OK, so it's long. But then again it does promise to analyse "the modern conditions of neo-liberal capitalism and the methods required to transcend it" and "provide an insurrectionary manual for those struggling to build a truly human civilisation." Not bad for 27 minutes!