Very funny the part where poor Nage goes around Uke, stop to rest then retstart running, restop to rest...all to reach the back of Uke.
Now, for sure what Doran Shihan says is right 100%, but I am sure this part of video is taken out of context.
You do Iriminage like the first video, doesn't mean that the cut down is wrong because the body knows out react.
The Iriminage in the first video is an Iriminage done when you might have a second opponent behind Uke, thus you really don't want to go behind Uke and give your back to the opponent.
Yes, legs and body do know how to react to a force going down and that's what makes Iriminage work. If you start iriminage on me and my legs didn't know how to react, I would simply go all the way down and stay there...result forget iriminage and do something else. Iriminage is possible because Uke tends to get up (either you help him a little or not).
I found wonderful the suggestion of "reaching for the other shoulder", it really put a picture in my mind of the arm movement...thanx.