Is there any way to slow down those youtube clips?
413, you are correct - some people have an innate sense or unconscious ability to correctly use their core - basically they do not need to think about it. For some runners, they have no core awareness - which can be trained by having someone show them proper core exercises all while telling them what they should be feeling and where they should feel it. Once someone "gets it" ... like learning to ride a bike ... then he or she can go about increasing endurance, - but until they "get it" there isn't much that can be done. Many people may have a strong core, but are not aware of how to use this strength. Proper core utilization essentially makes the trunk more rigid, pulls the hips into correct alignment and allows the glutes and hips to do most of the work. In this scheme, calves basically only add a very slight push and are used for their role as stabilizers - notice the calves of many of the Kenyans and Ethiopians - very, very small because they are not being used as primary "pushers".
The whipping or snapping of the legs forward is facilitated by strong and flexible hip flexors and glutes. The knees are really driven upwards by this action and not actively lifted.
Imagine hitting a baseball with a bat made out of rubber - energy gets absorbed by the bat and the ball does not travel very far when hit.
Also, with good running posture - the legs are essentially able to "freewheel", "spin" or as 413 pointed out "move freely" and energy is transfered easily from leg to leg almost like a wheel - hence my choice of the word "freewheeling". The wheel analogy only goes so far because a certain amount of "pogo sticking" occurs. There has always been some discussion about running being like a wheel or like a pogo stick - perhaps a wheel made out of pogo sticks would be the best thing to envision.