No you won't be challenging a demon to a skate-off. What executive producer Marty Stratton means is that the game encourages constant momentum, and gives players plenty of wide open space and options for vertical movement.
"You do have to get into these expansive tracts, these big spaces, to really let the player have that level of fun,” Stratton said, in an interview. “And even there we’ve kind of added a level of verticality to our game. We’ve added double jump mechanics and mantling that gets you up really, really fast.”
Thus far in the various trailers and clips released for the game, like the E3 clip above, we haven't really seen that kind of verticality, but Stratton says the game offers multiple opportunities for you to get the drop on the enemy.
Well that certainly sounds better thanwaiting for demons to jump out of cupboards, though I'm not entirely convinced that hardcore fans of the series will be that excited about being able to clamber around the maps. I associate Doom with tight, focused level design, which is hard to do when you open up the environments too much.
DOOM (the capitals are important) is tentatively scheduled for a Spring 2016 release on PC and consoles.