I think you misunderstood what this video was about. They were not explaining anything about the structure of the earth nor were they talking about measuring it.
The topic was the spherical geometry you get when trying to describe the properties of the surface of a circle crudely said as seen by a being that has no understanding of the third dimension and lives on it's surface.
So basically spherical geometry is needed to explain the measured distances and angles for a flat earth (for small areas euclidean geometry remains a good approximation).
When looking at it in three dimensional space you realize it is a sphere in euclidean space.
Also it is actually possible that our universe isn't flat (follows euclidean geometry) but curved meaning euclidean geometry would be the "not real" one.
(This is general relativity so if you really wanna understand what this means be prepared to spend a good amount of time on researching an understanding it as the mathematics behind it is quite complex.
Our current estimates make it extremely likely that our universe is indeed flat though.)
*Edit: removed embedded video from quote
The topic was the spherical geometry you get when trying to describe the properties of the surface of a circle crudely said as seen by a being that has no understanding of the third dimension and lives on it's surface.
So basically spherical geometry is needed to explain the measured distances and angles for a flat earth (for small areas euclidean geometry remains a good approximation).
When looking at it in three dimensional space you realize it is a sphere in euclidean space.
Also it is actually possible that our universe isn't flat (follows euclidean geometry) but curved meaning euclidean geometry would be the "not real" one.
(This is general relativity so if you really wanna understand what this means be prepared to spend a good amount of time on researching an understanding it as the mathematics behind it is quite complex.
Our current estimates make it extremely likely that our universe is indeed flat though.)
*Edit: removed embedded video from quote