Cool video. I'd like to work with that fellow. I've never tried to cut a tenon only with an axe, but why not? I'll give it a try.
The way I do it now requires saw, axe, mallet, and slick.
handsaw shoulder, align edge of axe with cheek line on endgrain and whack with mallet. Score cheek lightly with axe, finish with slick.
It goes really quick, especially in straight grained stock.
Whit