I think the TL video from :41 on shows it well, freeze the vid and look at the distance from his outside shoulder to his inside knee when he is next to the gates. Now go to the frame with an arm extended. His ability to get the upper chest on the side with extended arm down toward the inside hip and foot as he compresses into the turn.
the rolling movement vid is a way to check if you have
1. the trunk mobility to even get there.
2. if the extended leg is being held up in the air it shows you how tight your pelvic region/both hips
3. difficulty with the arm extension shows the difficulty in the joint freedom between the lower spine and the upper spine
4. Maybe the most enlightening is it demonstrates the dominance in your body, can't roll to the side your flexors aren't strong enough to overcome the extensors, can't roll back, reverse the pattern.
5. the more you have to use you legs and arms to perform the sequence the less of them you will have available for power where you want it.
there are other factors I'm sure we could tease out
the asymmetrical trunk motion(shoulder to opposite knee)whether in bending or extending, is a more primitive movement pattern for us, it is actually a reflex we have to learn to control, it's availability in our skiing/walking, etc allows for quicker movement and preserves the limbs for making adjustments along the way