That was an awful, awful video, I felt sick watching it. Especially now I know that the daughter has a disability. Clearly the guy is a raging psychopath who should be immediately disbarred and dismissed from any position of responsibility whatsoever. I guess he wont be charged because of the statute of limitations that fanofdo linked to above which sucks. At least his career will hopefully be destroyed and this is the only thing that people remember about him.
I'm not a parent, nor do I especially want to be in the near future, so I don't know much about disciplining kids, but I think it's pretty clear that that video was abuse. Everything about it, from the psychotic threats, to the repeated lashes with the belt was abuse. I do think, in some cases, corporeal punishment is justified, but that's not what that was. A spank to a bottom of a kid whose misbehaving repeatedly is warranted provided the mother/father is clear about why they're doing it, and takes a step back, gets the worst of their anger behind them, and then administers the smack in a calm, rational manner. Never out of anger or hate, or frustration. Which clearly was the case here. It's a bit of a slippery slope, and on the whole, I would say avoid the issue completely by finding more productive ways to discipline your kids. And the mother is every bit as culpable as the father. Being an enabler of abuse is just as damaging and cowardly as being an abuser, IMHO