I think "solving" isn't the right word for what they have accomplished wrt checkers.
1. They've shown it is possible to play any game to a draw, or a win if the opponent makes a mistake.
2. They've codified a "perfect" computer player - one which never makes a mistake and will always win or draw.
Thus, they've effectively reduced checkers to tic-tac-toe. (Or Global Thermonuclear War . . . )