My intuition rings false on this -- I don't think this is right. In a vacuum, ignoring the rocket equation (that is, assuming ejected reaction mass is negligible compared to projectile mass), the energy required to produce the 120 -> 96 mph change is the same as that required to go from 24 -> 0. This works out in conservation of energy because the ejected mass has kinetic energy of its own.
In the case of you landing, I don't think energy balance is the way to look at it; each of the collisions that slows you down will transfer some energy to the ground. In terms of force, the force is dependent only on the acceleration, so it comes down to how long each impact lasts. If each "bounce" or "thud" lasts the same amount of time (I don't know if this is realistic) then each one will transfer 1/5th of the force, as the article says.
In the case of you landing, I don't think energy balance is the way to look at it; each of the collisions that slows you down will transfer some energy to the ground. In terms of force, the force is dependent only on the acceleration, so it comes down to how long each impact lasts. If each "bounce" or "thud" lasts the same amount of time (I don't know if this is realistic) then each one will transfer 1/5th of the force, as the article says.