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.
Watching that clip again, I noticed something interesting. This way of delivering nikyo is very similar to the way I am used to doing it. Anyway, if you look at the moment when the pin goes on, you can see that there is a moment where uke's arm briefly starts to buckle, before the rest of his body starts to move. I think that it is this "wave" of buckling that causes the pain in the wrist. Personally I try to avoid this kind of delay in application - my ideal is where uke's body is locked almost immediately, and you have a direct control over your partner's structure through the arm and shoulder skeletal system.