Midnight Resistance

Midnight Resistance (ミッドナイトレジスタンス) is a 1990 arcade game developed by Nihon Bussan and published by Data East. It used a 3D joystick (a normal 8 way joystick that could also be twisted as a dial) to allow the player to aim independently of his direction of movement, which was notable at the time. The players take control of two commandos, Geoff Hunk and Dave Butch, who are out to rescue their kidnapped family, including their scientist grandfather who is being forced to create a weapon which will give the antagonist of the game, known only as "King Crimson", the power to take over the Earth.

Story
From the Atari ST/CBM Amiga manual:

A ruthless Commissar, leader of a vicious regime of megalomaniacs, has idnapped your family (including your Grandfather - a world famous scientist) in a desperate bid for dictatorial power over the earth. Can you rescue your relatives before the evil Commissar forces your Grandfather to use his superior weaponry research in order to enforce his own tyranny throughout the planet? Pit your wits against an obsessive army, their tortuous traps and a convoy of menacing machinery.