To me the essence of 2016 is the scene in the beginning where an info screen tries to dump exposition on you and you chuck it into a wall.
There is plot, but you don't need to pay attention to it. Doomguy is angry and needs to kill demons.
To me a big fumble in Eternal was trying to explain why doomguy is angry and so good at killing. He's like an inverse Cthulhu, terrifying, unknowable and mysterious. Trying to explain or understand him breaks the basis for the character.
On gameplay, I didn't mind the changes, but I thought the embellishments were a little on the nose. The technicolor rainbow explosion of ammo when you chainsaw someone, and the increased focus on using abilities to replenish resources scream "This is a video game!" in a over the top way that I felt took away from the immersion and grit that I associate with Doom.