This is the 1970 board game Ploy by 3M Bookshelf Games. It is complete with instructions.

From the back of the box:

Ploy is the stimulating space-age strategy game. The object--to eliminate the opponent's Commander or all of his forces. Since pieces only move along paths in line with the indicators radiating from their centers, the strategy lies in knowing when to move and when to rotate a piece to change direction. For 2 or 4 players. Bookshelf case contains four sets of spacial playing pieces, futuristic playing board and instructions.