Wrong. Team fortress was first. You could easily say that Quake influenced Half-Life/Counterstrike as well at least technically speaking. Quake should be #1. See my argument below.

Quake is still the most influential game ever, even more than Doom. You can dispute these reasons because they're just off the top of my head.

1) First fps you could play online

2) First fps that used mouse and keyboard (no more pgup pgdown keyboard looking)

3) First online squad based shooter (team fortress addon)

4) Quakespy anyone? (Where Gamespy came from)

5) GLQuake, one of the first fully 3d rendered fps

6) There are a lot more reasons associated with the design of a full 3d fps

FPS = Most popular game type ever
Quake = Most innovative FPS ever
Quake isn't on the list, therefore the list is an epic fail.
Logic ftw.

Best janitor breakroom ever?