Ah, cool, I wasn’t aware of arcade machines using recorded video before the brief laser disc era! If you have any references or links where I could read up about them, I’d be fascinated to learn more!
I don't know if the game my dad remembers worked the same way, but as you can see the footage is divided into two halves: the top half is the footage of the plane flying, and the bottom half has both a spot of light and footage of the plane exploding. A mirror inside the machine normally is positioned such that it reflects only the top half of the picture to the screen. The spot of light on the bottom half corresponds directly to the plane's location in the top half; a light sensor corresponds to the gun's motion such that when the gun is pointed at the plane, the sensor will pick up the spot of light (similar to the NES Zapper) and register a hit. Then at the right moment, if a hit was registered, the mirror will rotate, shifting the image from the top half of the film footage to the bottom half and showing the explosion sequence, before resetting for the next plane.
That's so clever! I would have guessed that film reels would be too fragile for that sort of continuous usage, though I'll confess that I have no personal experience with them.
I was really curious about how they would handle 'rewinding' a film reel between plays; assuming 16mm film, I figured, it would have been about 30 meters of film, so I wondered whether you could splice it together into a full loop and concertina it inside the cabinet so that it doesn't actually require rewinding between plays, and can instead just keep playing it continuously in a forward direction, and... after a bunch of Internet trawling, I found a forum post by somebody who had purchased and restored two units, that's exactly what they'd done! (I had my calculations about the length of the film wrong, though; apparently the full film is only about 10 meters long, which would definitely make it easier to wrangle the loop!)
The world of these older electromechanical arcade games is seriously cool; so much history and ingenuity here that I hadn't been aware of!
I'm older than you think (and so is my father). The arcade machine he played dates from the 1960s, and did not involve a computer.