I think his idea of shooter is "scrolls by itself, either vert/hor/diag, you shoot everything that comes at you, there is probably an ending". If we include every game from the 70s and 80s where you shoot something...that would be about %95 of the games from that period. Centipede, Bezerk, Space Invaders, etc are not shooters. Defender and Chop Lifter are *almost* shooters. Fantasy Zone pretty much is a shooter. Even though the user controls the scrolling, there is nothing to do but shoot. In other words, when you buy a "shooter" today, from Cave or whoever, the types of shooters that the PCE, Saturn, and DC (and now, 360) are famous for, that kind of game. They first really came to form in mid-late 80s.
I'm pretty sure Vanguard was the first shooter if this type. It scrolled by itself and even had an ending (which was just a vertical bar that said "END" in big letters. When you touched it the game was over.
Not shooters:
Battle Zone
Hogans Alley
Doom
Ikari Warriors
Space Harrier
Hyperball
Asteroids
Shooters for sure:
Aero Blasters
Zaxxon
Side Arms
Xevious (even though it suuuuucks)
Gate of Thunder
Ikaruga
Twin Cobra
Grey area:
Choplifter
Fantasy Zone