[If you missed it, check out last week's game as well.]
The famous game designer,* Sid Sackson, had over eighteen thousand games in his personal collection so making his short list was quite an accomplishment, particularly for a game that almost nobody has ever heard of.
On this alone, the Blue and the Gray would be worth a look, but the game also has a number of other points to recommend it: it only takes about three minutes to learn (you can find a complete set of rules here); it is, as far as I know, unique; it raises a number of interesting and unusual strategic questions; and for the educators out there, its Turn-of-the-Century** origins provide some opportunities for teaching across the curriculum. My only major complaint is that it requires a dedicated board, but making your own shouldn't take more than a few minutes.
The object of the game is to be the first to get your general to the center by moving along the designated path while using your soldiers to block your opponent's progress. Since soldiers can capture each other, the game has two offensive options (capturing and advancing) compared to one defensive option (blocking). (Something I learned from developing my own game was the more the designer can shift the focus to offense, the better and faster the game will play.)
I don't know of any attempt to do a serious analysis of the Blue and the Gray. Might be fun to look into. If someone out there finds anything interesting, make sure to let us know.
* Yes, I did just use the phrase, 'famous game designer.'
** I'm going off memory here about the age of the game. You should probably double check before building a lesson plan around this. (see update)
Via the good people at the University of Maryland, here's the original patent from 1903.