All The King's Men

From BoardGameGeek:

This is a strategy game similar to chess. The board is layed out like a chess board and each player sets up their men just like in chess. Unlike chess, the board for Smess has various types of arrows printed on each square of the "chess" board. Movement is determined by the direction of the arrow or arrows in the square. The pieces are similar to chess in that the Brain is like a king in chess, Ninnies are like pawns, and Numskulls are like rooks or bishops. This is a fun game that is much simpler than chess at first glance. However, the game will vary in difficulty depending on the skill of the opponent. The goal is to capture your opponent's Brain. The fact that both players can "see" all possible moves to and from a square can make the game harder than you'd think! A fun game! The game was later released with medieval themed pieces under the title All the King's Men.