This game is Anglo-American Checkers (Draughts) with a special board and somewhat more powerful Kings. The edge squares of the board -- marked with diagonal lines -- are special. They may only be landed in as the result of a capturing move. King can move and capture diagonally forward and backwards, and capture (but not move without capturing) up, down, left and right by a jump of four squares, landing on a dark square.
 
The ring board was inspired by the rule found in some of V.R. Parton's Checkers variants, such as Kinger and Dragon, that some pieces may only land on edge squares if that is the only way to make a capture. The King's orthogonal capture was inspired by Frisian or Babylonian Draughts, which allows such captures.