No, they're a different genre. The one you're talking about is referred to as 'action.'
In DMC you run into a new area, then you're surrounded by a group of badguys with whom to deal out a few close range attacks, and you move on through a fairly linear game that is broken into stages. "But DMC has guns" you say. Even the original Double Dragon has guns. You level up and gain new moves, just like Double Dragon the NES. And didn't Dante have to fight off his evil brother just like Billy did? About all DMC lacks is a disembodied hand pointing you where to go next.
There are similarities, but you might as well try to claim that modern Ninja Gaiden games are platformers since they have some jumping.
Except the primary concept behind NG isn't jumping, it's melee combat. Hmm, now that you mention it... DMC's and Ninja Gaiden's jumping mechanics are just about as janky as Double Dragon I & II's.
Please don't mistake this post as saying Double Dragon and DMC are the exact same, because they're not. Rather that DMC is an evolution of Double Dragon's core concepts. People seem to be locked into the idea that a beat-em-up has to a 2D sidescroller. They've evolved just like every other genre has.
Edited by Thrinn, 11 February 2012 - 05:03 AM.