I actually didn't realize there was even room for debate that it was a continuation/sequel to 1.X. The storyline clearly continues from the original, they reference it continually, not just in dialogue or storyline, but in the world as well. The giant flamey orange crystals you see scattered all over the place (especially in Thanalan) were remnants of Bahamuts attack, Gaius' assault on Eorzea is a continuation of his work in 1.0 before Nael showed up and took over things, and there are a lot of returning characters that have changed since.
If nothing else the addition of Cid's facial hair shows it's a continuation!
If nothing else the addition of Cid's facial hair shows it's a continuation!