At 7:00, you said to extrude along the z-axis by using "e+gz", extrude, grab, and lock to the z-axis; was this meant to be "e+z" as in extrude and lock to the z-axis? What is the difference?
Whoops! Yes, this was meant to be "E followed by Z". You can see this key combination reflected in the key logger in the lower right corner of the 3D viewport.
Something is going wrong for me at this point. I'm not getting the diagonal extrusion.