From what I can tell people don't know what they want, they do know that they don't like anything they get though.
There's not likely to be a consensus on what a 'proper' Doom reboot is likely to be. We can all pretty much agree it has to fast, have X Y and Z guns, and feature the monsters we like, but how that all comes together, and how the moment-to-moment gameplay works, I doubt it's possible to please everyone on that front.
There are some people, rare as they are, that think Doom 3 was a good direction for the series, after all.
What they have seems to be a mix of Doom 3 (visuals), Brutal Doom (the melee mechanics), and Doom 2 "stuff." It's definitely more centered around the action than Doom 3 was, and the visuals are significantly better than Doom 3. The melee executions need to be a mechanic that are used more sparingly (only way to get health would work -- as it turns the move into a comeback move that can keep the flow/pace moving forward instead of backward).
I'd like to see the impact of the weapons do more, the sounds on the plasma gun to be massively enhanced, and the melee executions be purposeful and in the service of the 'forward momentum' they are trying for. I want to see the shaders changed so that you can still make the contextual executions, but not so visually ridiculous. It would be nice to have a bit more color in the enemies to differentiate them. The designs seem fine other than that, and the speed of the game seemed okay too in the second part of the demo.
Maybe they should just turn the melee mechanic into a resource that fills up occasionally. Have a meter or something so you can use it once, then have to kill a certain number of enemies to be able to do it again. That's the major complaint I have -- if it's not used in a smart way, it *will* become a chore after a while. I mean, does anyone who plays Brutal Doom actually use the mode that much when they pick it up? I did for a bit, but after a while I stopped because it didn't really give me anything.