It's a complete 180 from Doom 3. I've tried to play Doom 3 a handful of times in the last decade. I never once got to shoot anything because I didn't have the attention span to get through the 30 minute intro/story/tutorial.
Sometimes you just want to shoot demons because they are demons. There is story in Doom but it rarely prevents you from continuing to send demons back to hell for more than a few moments. There's more in the menus but those can be read at your leisure.
If you're up for some traditional Arena FPS, take a look at Reflex, Xonotic, and UT4. Or just boot up Quake 3 (or Quake Live) again.
I almost forgot Half-Life Deathmatch. That's still an absolute blast to play.
Very interesting. Found this video gets into some of the details of strategy: https://www.youtube.com/watch?v=DIZ-PhgPLOY