Welcome to the 1980s! This is probably the most influential era in video game history. In the 1990s video games became more like cartoons and books; in the 2000s and 2010s they became more like movies but in the 1980s games were kind of doing their own thing. For instance, if you came across Battle Zone back when it was new you'd probably be forgiven if your jaw hit the floor.
Battle Zone is an FPS. One of the first, in fact. You control a tank and use it to battle other tanks in a first-person three-dimensional environment full of debris that you can use as cover. While I might not have felt all that inspired by some of the classic games from the 1970s, I really understood why Battle Zone is on the list once I started playing it. This is a game that was ahead of its time - back when games were largely about the wonder of controlling a little man on a screen, this game gave you an entire virtual world to roam around in.
Incidentally, Battle Zone had a pretty sweet remake for the PC in 1998 that was more of an RTS/FPS hybrid. It was very cool and certainly worth a look if you're into retro PC gaming.
The version of Battle Zone I played was Flash-based and is available for free on Atari's website. I was unable to get this game to work properly in MAME, but insofar as I can tell the two versions are identical in gameplay.