Several retopology operations in the video are possible with this PolyQuilt add-on.
Operations such as movement, extrusion, knife removal, loop cut, etc., and their symmetrical editing can be performed only with the left mouse button.
As it is still beta version, I think that there is room for improvement if you support developers.
PolyQuilt | Blender Lowpoly addon for Blender2.8(beta)