Dunno if any of you have actually covered this or not(had tl;dr syndrome), but the way I see DmC is a reboot in a way where we're looking at the reboot as an alternate universe type setting. Granted, some aspects are still the same, at the same time, it gives a bit more closure on the story...well, making sense. For example, the term nephilim being used as Dante and Vergil's labels in terms of species. Instead of being half-demon/half-human/half-breeds, they are the forsaken offspring of Angels and Demons, children that are shunned by either side simply because of the potential they hold that can overthrow both Heaven and Hell.
Instead of Dante being the usual gothic guy running around slaying demons as a job, he's a thuggish kind of guy with the same sarcasm, but being pulled in to do it because it's his responsibility(and he actually cares). I suspect with the Vergil's Downfall DLC, he will more than likely be going through his own actual storyline where he probably falls to the Underworld, and undergoes his transformation to become the Dark Knight/Dark Angel, Nelo Angelo. And of course, there are speculations on how some of the enemies are personifed, i.e, the Succubus in 'Secret Ingredient', and one of the creatures called 'Nero' later on in the game, where it's rumored it might be DMC 4's Nero BEFORE he attained a human form.
Can't really say this is all true, but logistically, it all makes sense. It's just up to the producers to confirm it.