Deflections

Deflections is a 1985 game by Nik Sewell, published at Pentagram Games.

the centerpiece is the energy gun that shoots projectiles 

The game uses projectiles that move through the board, reflecting on different types of walls. These projectiles keep increasing in numbers, until one player is unable to escape thus losing the game.

 the different types of pieces and shields 

Here are the original rules (click to expand) explaining the rather convoluted rules of projectile movement.

This seems like a game more appropriate to be played on a computer. Updating many projectiles with difficult update rules is a recipe to constantly create invalid positions.