If you watch, you can see that Young is not using Duke to push off from horizontally, Duke is helping him to lift up vertically. Therefore the bulk of the force is travelling vertically through Duke and doesn't cause any appreciable sideways motion, either in Duke, or in Young's feet. All Young needs is enough grip on one foot to maintain a pivot point until he can get upright, and he seems to have that with his right foot. Again, also, in 1/6th g., it would be easier to lift your body weight using just your upper arm strength, so there's less need to brace or tense than you would need in Earth gravity, and a correspondingly less obvious reaction as well.