I think the video was mostly a bit funny but don't really know enough of the history of the family to make any judgment about whether the punishment was fit or the source of the problems (chicken or egg). Among the parents there has been a failed marriage, so that might be some clue, but a kid can just use that as an excuse as well. I had to do chores, a lot of stuff that I hated, but I saw the benefit of it and viewed it as necessary and think the chores made me learn the value of work. Many of us work to earn money, primarily, but it's best if we can also strive to make our world/community a better place.
The girl had been grounded before and her response was her little tirade that the father read. Grounding her for two weeks from the computer is not sufficient, IMO. I don't consider shooting the computer "violent". Some folks are just too afraid of guns. Guns are not a problem anywhere, it's bad people with guns or other weapons that are the problem. I lettered in high school by being on the rifle team. I don't think poking holes in paper was more violent than boys elbowing an opponent in basketball or sacking the opposing team's quarterback. I think shooting the laptop added some fun drama to the video is all.
Parents owe their children love. Children owe their parents love and respect. My son turns 14 in a few days and gets a bit testy at times but that's part of learning independence as boundaries are tested, but we've not had any serious issues and we're confident he's going to be a fine citizen. I've got a tomato project lined up for him this summer (to sell tomatoes to a couple of local outlets) and he's looking forward to it and not whining.
