Agree with JackSprat's mom...I think SH's idea is to be able to use (this) exercise to create an honest response, not just 'hope' the horse is relaxed (in the walk or work desired). So using leg yield is an access point to check in that the horse honestly "allows" you to use your aids- not aggressively or in a worried way as he says but in an easy way...here in the walk. The walk will then become relaxed and rhythmic through the horse's acceptance of the rider's (leg yield) aid.
Very hard to get full message from a short video.
I tried this exercise today with my young horse. I found it useful and def made him wait and listen for me and stay relaxed in his work.
The transition was engaging, the LY was suppling to encourage relaxation and gain access to the horse.
I agree with whoever else said the saddle looked awfully bouncy. Perhaps a properly fitting saddle would relax the horse too instead of BOUNCE BOUNCE BOUNCE all the time.