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He probably means the kind of games that my schoolfriends and I played in the eighties, in which each player had control of a large group of districts represented by cells that might be regularly tesselated but might be of irregular shape and might even be subject to dividing into smaller cells by the building of e.g. canals through them. In these games every move would be either a single step across a border or (in more complex versions where railways could be laid) several such steps along the line. Orthogonal directions are the only ones carrying through to these games from Chess.