I love electromechanical arcade games. My father mentioned one from his youth that had you manning an anti-aircraft gun and shooting down incoming WWII fighters. This would have been made in the 1950s or maybe even the late 40s, given the time frame at which he played it.

I managed to find a game that was conceptually similar, but certainly not the game my father played. It was Sky Hawk by Nintendo, made in 1976:

https://m.youtube.com/watch?v=2GMAWtqJr3w

The way it works is there are actually three clips of footage: plane attacking, plane exploding, and a light spot indicating the target area needed to register a hit. The latter two are shown on the bottom half of the film frame at different times. A mirror usually reflects the top half of the film, showing the "attacking" footage, toward the screen where the player can see it. However, the gun is mechanically linked to a light sensor pointed at the bottom half, and if it picks up the light spot in the "light spot" footage, a hit will be registered. When the "plane blowing up" footage starts, the mirror will pivot to reflect that to the screen instead, and you will be awarded a point.

It was an ingenious setup that required no computers to operate. It was pure mechanics and optics.

Another difference is, Sky Hawk used footage of R/C model planes to simulate the incoming fighters. From my father's description, the game he played used footage of actual fighters taken during actual WWII engagements. But the idea is the same, and it makes me wonder if a similar mirror setup were used in his game as well.