I just saw this show and found this thread on the googles. The things I can think of are:
The show was no doubt edited to have the animals fall asleep faster than they actually did. Was minutes or hours cut? There's little notion of time passed.
The alpaca farmer used the terms "unusual", which does not imply anything supernatural. It was "feeding time", but I didn't see them actively eating, being all gathered around the same tray or something. Perhaps they fell asleep some time after eating. It looked warm, perhaps the animals always go down like that for their Siesta in the middle of the day.
As someone mentioned, perhaps the animals were simply fed sleeping pills. The sensei, the producers, the farmer, as much as I'd like to believe they wouldn't have, they might have done so in order to make it a more dramatic recording, which would be in all their interests.
Normal animal empathy/communication. If you look at a cat and squint your eyes, chances are it will squint back or close them. Perhaps herd animals like those in the show share habits like this.
Animal hypnosis.. I know next to nothing about this topic, so I won't speculate on it.
So I would repeat the experiment, at least controlling for these factors:
Provide the animals independently
Do it at different times of day
Different weather, temperature
Does the qi powers depend on visual contact? Put a wall between the animals and the sensei
Control group of animals to see that they don't fall asleep
This is nice. Founded by father and son Oscar and Cristobal Scarpati, the Doma India School in San Luis, Argentina is using yoga to tame and relax nervous and traumatized horses. According to the Scarpatis, yoga helps form the bond between the trainer and the horse, making it possible to tame and teach the animal.