What I get from their explanation is that hexagon is a better shape for map grids because they are the most complex shape that can tesselate (the other two are triangles and squares). As they are more close to a circle, distances within a cell are more stable, also computing the distance from a cell center to its neighbours is stable in hexagons as well.
I think the reason hex is not more common is that subdivisions are hard to create compared to triangles or squares. Uber solved this by subdividing in 7 smaller hex and tilting it so they cover the bigger shape with some small overlap.
Also a big problem is distortion, I never thought this would be that huge of a problem but it makes sense. They go into a lot of the details later on the same video.