According to this article on Kotaku, H.G. Wells invented modern tabletop wargames. War games had been going on for a long time, but Wells was the first person to make them accessible for a casual, non-military audience with his game Little Wars.
Here's a picture of some people setting up a game:
And here's a drawing of Wells playing at home. Depending on what year this was drawn, Wells is either the gentleman in the bottom left, or the older man sitting in the chair.
Strange, isn't it!