To clarify: war-games can imply two things: in a modern context, it could refer to table-top gaming as you implied. However, it can also mean military exercises. Do you know which 'war-games' makes the most sense in this context?

Fred T. Jane wrote the creatively titled "The Fred Jane Naval Wargame" in 1898, roughly the same time as his publication of the first edition of Jane's Fighting Ships, and an updated version of the rules was included the 1905/06 edition. If I remember correctly the stats for various ships in the game were derived from the specifications in the book, although how long the rules remained bundled with the book, I am not certain.

Having never tried the rules, I cannot give a review of them, but from the few reviews from others that I have seen, it is a reasonable mix of abstraction and realism, the key unique feature being physical "strikers" used for randomly determining hits. The rules were for the pre-dreadnought and early dreadnought ships of the day, although Fletcher Pratt wrote a set of rules in 1940 that preceded the 1941 edition of Jane's Fighting Ships (which came nearly 17 years after the previous) which appears to be somewhat similar, but built for the fleets of early WW2.

The History of Wargames site linked above does stock reprints of most vintage wargaming rules and periphery, so it is possible to recreate them.

As mentioned in another comment, wargaming can refer either to military wargaming (which is for the purpose of developing strategy and tactics that will be used in real military conflict) or civilian wargaming (what you're most likely thinking of).

Civilian wargaming grew out of the Prussian military wargames (Kriegsspiel) of the late-19th century. As for the kind of games Jane played – he developed his own rule set. You can view Jane's original wargame on Google Books here.

Another popular civilian wargame of the era – this one dealing with land-based war – was created by H.G. Welles, with the stated purpose of showing civilians how horrible war was. It was called Little Wars.

There's a good article by Lt Col Matthew Caffrey, Jr. in the Fall 2000 issue of the Aerospace Power Journal called Toward a History-Based Doctrine for Wargaming that deals with the origins of wargaming and its transfer to civilians. You can read it online here.