From Bethesda VP Pete Hines via Shocknews:
"The biggest problem we thought we had with Doom 2016 was that [multiplayer] wasn't done at id, and felt really disconnected from the base game that everybody loved… Whether you're playing by yourself or with others, we want it to feel like you're all playing the same game. That's as opposed to, ‘I'm a badass demon slayer in singleplayer, but when I go over to multiplayer, there are no demons, and it's just Deathmatch.’ I don't know what that has to do with [Doom] other than that, well, a couple of decades ago we had that, so we should just have that again.”
So basically, they don’t feel like “tradition” is a good enough reason to include a mode that, let’s face it, is pretty dated these days. There are a lot of deathmatch and competitive shooting games out there, and while not all of them have the same run-and-gun “feel” of Doom, it is also true that “run-and-gun” isn’t what people come to Doom for: they come to Doom to slay demons, and their new Multiplayer mode is far more on-brand, in that respect.
We don’t know if it’s any good yet, of course, but we’ll find out soon.