The first Doom 4 video is deliberately slow. The guy was taking his time walking around, looking at everything and showing off each weapon one by one. There's none of that in the second video and as you can see, it's much faster. Maybe not quite as fast as the old Doom, but that might be intentional since this game doesn't have the massive amounts of auto-aim Doom 1 and 2 did. Movement speed aside, my point still stands. You weren't constantly having hordes of enemies charging at you in the old games.
As far as exploration, it's too early to tell. That wasn't an actual level, it was a vertical slice, built specifically to show off on stage for a few minutes. Hopefully they don't overlook the exploration element in the final game.