It's not the same continuity, so no, it isn't a prequel. Original Dante and DmC Dante are literally two completely different characters (the former is half-demon, half-human, while the latter isn't even human at all, instead being half-demon, half-angel).
With Capcom claiming that it's possible for them to potentially continue DmC if successful, yet also bring back the main series, the question remains if there's any truth to what they say.