Well...I actually don't think that was an attempt at discipline. It seems more like a frustrated parent, tired of a child's attitude. From the words on the video, I'd say it was a single parent also. It sounds like perhaps that child in question might have tossed the other parent into the face of the mother. I also don't think this was a one-time issue either, based on the voracity of the verbal attack.
The parent seems to want an apology for something the child has done.
I don't say that I feel the screaming is the best way to handle it, but as a single parent with a child that sometimes throws "daddy" at me when I won't get her something she wants or won't let her have her way, I can certainly understand some of the frustration in the woman's voice on the video. In fact, she sounds as though she's been pushed too far one too many times. I also agree with Sci - what did that kid on the video do to warranty such a violent verbal response - a demand for an apology from the child?
Im not sure if the OP is saying that's him/her or that they went through this type of thing.
It's sad though, that the relationship between child and parent has devolved to that point we see in the video. Although my daughter is still young (she's 8 now) when she started behaving so badly that I found myself sometimes unable to control my temper to the point I'd yell at her, I took her to a therapist. After a few visits, he closed her case out. It seems that just a little bit of learning ways to deal with the stress of being in a single parent household really helped us both.
I still raise my voice to her sometimes, but it's usually when she's done something that could have hurt her.
Fear will make me yell when anger wont. lol
Ps. You know.... there IS such a thing as parental abuse as well. Not saying that's the case here, but I've seen that sort of thing way too often by children who either have no control of themselves or don't really care about the destruction they cause for their parent(s).