Didn't watch all of the the Mori video, but the Nikkajo he demonstrates within the first 3 minutes of that video is different than the one in the video used as reference in the OP. In the OP video, the shite's hands are close together relative to most versions of this type of wrist lock, and can readily work together in a manner that allows the degree of pain from the lock to be varied (i.e. the hand not applying the lock can manipulate the uke's wrist and forearm like the tsuka of a sword, supported by vs. supporting the hand applying the lock, if the shite so chooses). Here's the close-up shown in the video: http://youtu.be/QchlmrPnidA?t=1m30s
The shite also induces kuzushi by stepping forward to drive the forearm forward and down toward the uke's center as the lock's applied (again, the force can be transferred to the uke's arm primarily via the hand grabbing the wrist moreso than the hand applying the lock, if so desired).
These factors should allow the shite to execute the technique with little or no pain, if so desired, for demonstration purposes. And, based on my experiences taking ukemi for Yoshinkan practitioners, that is the case.
Nikyo whether applied by holding the wrist out in front of yourself or bringing it up to your shoulder is the same technique. What I am saying at least is that pain is Not the Primary means of control with this techniques, BUT it is a likely to be at least an outcome to some degree at some level, especially when done at speed, you know, real life, not the way demonstrated in that OP video
or the other for that matter. Although the application by Mori sensei seems at least plausible. Outside of a demonstration or the friendly confines of a dojo nikyo will probably be put "on" at speed, because someone say will really want knock your teeth out and its not an academic exercise for them. They just want to hurt you so if they grab you anywhere, most likely their other hand is already on its way to your face. Connection with Uke's center, (yes) is the main mechanism for taking their balance and the same with Sankyo. However, while one could theoretically do it without any pain at a slow and controlled pace as in the OP video, its highly unlikely 8 out of 10 attempts in a real life situation.
Also, one must add in the flight or flight response that Nage in real life situation would most likely experience when applying nikyo in real life where your adrenaline in pumping through your veins and the precise sensitivity you experience in the dojo a slow speeds or static will be elusive at best unless of course such confrontations are common for you. I am sure that many individuals on this message board can site examples of how anecdotal evidence in their lives differs from what many practitioners and Shihan such as Shioda have said directly in their own words. Indeed, we are talking about an art not chemistry so one can Always go to that card, because at the end of the day there are no absolutes in the martial arts.