After watching the tube, ...looked Ani up on Wiki.
The removal of rock ,....appears Chemicals are being used to hollow out segments .
Possibly the remaining sections can be broken away by leverage action.
The smooth curvature work could also be from chemical for final form finish.
The Church history in the region probably brought the Stone Mason guild knowledge with it.
IMO,...the more distant age when Giants existed, ...they too used Chemical to soften stone and remove that.
Geopolymer (creation of artificial stone) ,...this appears at Bosnian Pyramids, In Dynastic Egypt [youtu.be]
The drill bores found in Egypt. .from Giza to Abu Sir,..
These are machine advance with control to the millimeter.
Chemical bore would create high/low from chemical pooling and non machine feed rate.
So ya....the Ancients used Chemicals to work stone,
They also used advanced tooling feed rate machines,.....possibly Sonic cutting technology.