I figured it out when I was young, by closely looking at the screen when you fire up with the gun; the trick is that whenever you press the button, the screen goes totally black except for a small white square around the duck. Then the gun uses a light detector to check if what''s in front of him is white or not. If it''s white, then the duck has been hit, otherwise it missed. And all of this is done in 1/60th of a second, so you can barely see it.

I am pretty sure that''s the way it works, you could check that by setting the contrast and brightness level of your TV to the maximum level, then fire randomly on the screen. As far as I remember, it works great