the video doesn't have to do with kiai but shows the disillusion process ending with an injury. wonder how appologist students excused him out of that? He just had a bad Ki day?
I don't train vocal 'kiai'. but I see three common uses for it:
1. Demonstration dramatics (keeps the crowd and judges awake).
2. Tradition (for keeping up class spirit during larger group training. esp. kids classes).
3. 'War cry' (to invoke fear while releasing fear).
The sound used matters less than the emotion it seems to serve.
Technique-wise, a very short burst of air initiated from the quick contraction of the hara is suppossed to assist in training kime and sinking timed to breathing. after those principles are learned, kiai needn't be continued for that purpose.
Long sustained vocal dramatics from the lungs is just screaming....which is what most are taught to do.
Kiai at predetermined points in kata were arbitrarily set and became tradition when Karate was systemitized into Budo Art. do another sound or at other points in kata and traditionalists will tell you you're doing it 'wrong'....but they can't tell you technical reasons why.