It's a hard balance to strike, thematic purity with mechanical accessibility, and for what it's worth I think Rising Tide does the best that any game could hope to do with those two opposing forces as stated goals.
I can remember more than one occasion when I literally yelled out loud after I threw my gun into an opponent's face, grabbed his rifle out of midair and shot him with it. It's a game that doesn't need excessive achievements, unlocks, or leveling up, because playing the game well is so much more rewarding than any creeping XP bar could ever be.
The player, a gun, and things to kill. That has always has been DOOM, and id's legacy has been rekindled with DOOM (2016). You may argue that a good sequel's job is to iterate on past successes, to further develop mechanics, or to evolve a title to the next step in its life cycle. But DOOM (2016) isn't a departure or a reimagining. It's something much better, much more pure. DOOM (2016) is a homecoming. And boy, does it feel good to be home.