Yes, we need to be careful about panty-knotting.
1. Push hands is a training tool, as Xuesheng and Tony wrote. Not every training exercise or tool can be
directly applied "on the street," but hopefully can lead to increased skill in an area such as sensitivity or reflexes.
2. Yiquan, to me at least, is a kind of
conditioning for reflexes and full-body usage inside and outside a martial context. In my opinion, it is a terrific
supplement to other martial arts that teach techniques. This is what I like about Yiquan -- it's interdisciplinary.
3. As with all martial arts, anybody can say they do Yiquan, but it doesn't mean they're any good at it. We need to be careful about assuming that any martial art or technique, on its own, is good when we see someone do it well, or bad when we see someone do it badly.
As for the video ... Yiquan doesn't promise that we can do that sort of thing. It's quite practical, and the guys that I know would never try that. Is the video magical? Naah. In my opinion, if the student is really stiff and easily surprised, the teacher can maneuver him into a position where he can exploit the student's natural reaction to freeze, and cause the student to stiffen up because he can feel how the student would react, and knows what it takes to stiffen somebody up. From my small experience, I'd guess that the student is neither in pain nor electrically shocked, but is mostly
surprised by his body's unexpected reaction to being lined-up and pushed just right to cause overall stiffness. (Recall that Yiquan is about teaching full-body usage, so full-body stiffness makes sense as the reaction of a junior Yiquan student.) However, if the student were more experienced, were very sensitive and relaxed (and not intimidated by the master), this technique would not likely work. In that case, the student would not let the master find the right alignment, and instead would let the master's push slip aside, even just slightly.
That's my opinion: while it looks like magic or hokum, it's a sensitive teacher finding a student's alignment and surprising him so he stiffens up. Once the student goes stiff, it's easy to bounce him away.
(I tend to favor the naturalistic explanation.)
Oh, wait -- can stiffy-bouncy be used in a fight? Gah. Hell if I know. But I see the sensitivity training as useful: the master can probably read an opponent's movements pretty well once they make contact. It might be possible to surprise and freeze-bounce a stressed-out and angry opponent, but Yiquan also teaches you to just kick the knee (or stomp the ankle) and be done with it. Good Yiquan is efficient and practical: no woo, no magic.
Last word: not all videos are suggesting "you can use this in a fight," so we need to be careful about reading that message into them.