The coach in the video has some of the worst belay technique I have ever seen. Unfortunately, this is somewhat common among older climbers who learned using the first generation Grigri in the 90s. Petzl's recommended technique back then is very safe (essentially using the Grigri like an ATC), but does not allow giving slack quickly. This made it completely useless for any kind of ambitious sports climbing, and people started coming up with often extremely dangerous workarounds. Petzl has upgraded their recommendations a long time ago, but some people are resistant to change ("it never failed for me"...) Hopefully this video can convince at least some of them to finally adopt the proper technique.