The commercial offsprings of Chess: Ploy

Ploy, aka Imperium, is a 1970 game by Frank Thibault, published by 3M among other companies. 

The initial setup:

The rules by Mats Winther from his Zillions implementation:

The goal is to capture the enemy Commander, or reduce the opponent army to a single Commander. Each piece has an indicator which determines at which directions the piece can move. This can be altered by rotating the piece 45 degrees, left or right (a direction move). Rotating the piece costs a move.

Each player has three Shields, five Probes, six Lances, and one Commander. The Shield moves one step and has only one movement freedom at any time. The Probe slides two steps and has two freedoms. The Lance slides three steps and has three freedoms. The Commander has four, but can only move one step.

A player must either make a direction move or a motion move. The three Shields are the only pieces that can perform a direction move immediately after a motion move. Capture occurs by displacement

Winther also includes some tactical advice:

This game seldom ends in a draw. It is sometimes worthwhile to sacrifice material if you can gain an attack on the Commander. When the pieces become scarce, the Commander is more vulnerable to attack. As it can only move four ways, it cannot easily escape. The Lance with the three forward directions is especially suited to attacking the Commander. Remember that you can also win by capturing all enemy pieces except the Commander.

The game can also be played with Ludii.

The official rules:

Here is a review of the game at Games & Puzzles #22:

The game was seriously promoted as shown by this full-page ad in The General magazine #13:

There is a similar game, but played on a hexagonal board, Michael Flynn's Omnigon (1998):

More information about this game at chessvariants.com.