It's a direct continuation, though both Russel T. Davies and Steven Moffat have both retconned some stuff from the original run, the biggest one so far being the 13 regenerations limit.
That isn't an a retcon - a retcon is when they claim something has always been the case. So if they started the series and the Doctor had unlimited regenerations and the characters treated it as if that had always been the case, that would be a retcon. The Doctor gains more regeneration as a plot point via the intervention of the Timelords- it's not a retcon.