So I am a profound skeptic on ancient aliens, lost high tech civilizations, etc. Which is a polite way of saying I think it's total horse crap.
This guy seems completely unaware that "precision" can be achieved by hard work, profile templates, and lots of polishing. And while there were no dial indicators 5000 years ago, there certainly were fine wires, and there is nothing high tech about a surface gage.
I have no problem accepting a bodger-type pole lathe, manually powered, for rough turning, although granite is a pretty hard stone for that. Marble, on the other hand, would be easily turned with that sort of gear. But if this guy want us to accept a lost high tech civilization on the basis of a "precision turned" granite vase, he needs a better explanation of the integral handles, which obviously would prevent turning the corresponding band on the exterior. Of course, he'd probably double down and exclaim that's some sort of proof that the ancients had CNC technology because "that's the only way such features could be produced."