Firstly, many of the games in this category are Afican in origin and are commonly played in Africa or the diaspora so the the games would be able synergize well with any other Afrocentric content which was part of the school curriculum. (Some of these games are also popular in Asia. E.g, recently a friend of mine sent me a picture of a Malaysian coin which has the image of one of these games on one of its sides.)
Secondly, the games are almost purely "mathematical" in the sense that they are based on keeping track of the number of stones or seeds contained in various "pits" on a game board and so they will provide a certain amount of practice in counting, doing arithmetic, and certain kinds of mathematical reasoning.
To be honest, I'm still trying to figure out which particular mancala-game is the most mathematically rich for the purposes of teaching. Oware is one of the more "serious" versions and seems to be the most respected in terms of adult-play (e.g. The Oware Society holds international tournaments and keeps track of rankings.) Kalah is the most widely-marketed version in the U.S. (It was one of the games included on my first cell-phone and it is also the game included in the links below.) I've met a group of Haitian-American students who like to play a version of mancala which is basically a race to clear their side of the board. But there are literally dozens of variations. If anyone out there takes my plug for mancala games seriously, you might even consider starting clubs or organizations where young people could come together to become familiar with several different games instead of just focusing on one.
Mancala (3 stones per pit)
Mancala (4 stones per pit)
Planet Grenada on games:
weeping and nashing of teeth aka he got game