It doesn't have to be too confusing. Sadly, the video shows the 'uninteresting' version of the ADD system. If the diff side stub was spun, you would see the side gear out to the ADD sleeve spin opposite direction from the side with force applied.
Here are a few situations:
Driving slowly, 2WD: Driver's side diff side gear spins with CV axle, disconnected side spins opposite direction, ring/pinion is stationary. At the ADD sleeve, the two 'sides' are going equal and opposite directions.
Driving quickly (say, freeway speeds) 2WD: Same as above, but enough viscous force is applied to the ring gear/carrier by the spinning side/spider gears that the ring spins a bit. The prop shaft will spin, but much slower than it would if the ADD is connected. It is free to move at whatever speed it 'feels like'.
4WD: Everything is locked together, uninteresting for this discussion.
Shifting into 4WD while moving: The ADD system does not engage until the transfer case shifter is in the 4WD position. There is a synchro on the 4WD shift sleeve in the transfer case, which applies torque to the front prop shaft to spin it up to the speed of the rear prop shaft. This is why as the transfer cases get older, they get harder to shift into 4WD - the synchro gets worn out! When the front prop shaft and the left CV axle are spinning at the same speed, the right diff output will also spin at the speed and direction of the right CV axle/stub shaft. At this point, the ADD can engage without trouble (the splines are are basically going the same speed).
Hopefully that clears it up a bit.
-Charlie