I also noticed that he had the ax tied with a lanyard to himself. That seems like a great idea in case you lose your footing and drop the ax, You might be able to recover it before sliding down a slope.
Tying your axe to your body prevents losing the axe, but if you fall and drop the axe, it may beat you to death while you tumble down the mountain. I usually use a leash around my wrist. It should be the right length for the two-handed self-arrest or for swinging the axe with one hand.
