From the video, and the added statement, I get the general impression that the daughter had many a chance and had (essentially) a life of luxury. And like most teenagers, thought their respective lives were "ever so hard" - the same stereotype usually self-applied to the Emo types of this world.
As it is she's 15, hasn't a clue and puts up a nasty post on Facebook trashing her parents and the woman who comes to help out with the household chores. In the end, its not about who the post was aimed towards, but the content and the vile nature of it. If she isn't suitably chastised, then she'll "forget" and whatever punishment that was metered out also forgotten. Which, apparently, did happen in prior instances of her poor behaviour.
But don't get me wrong, my knee-jerk reaction can be summed up as "Crikey, that's a bit much!" but I watched the entire video and read the statement to put together as much of the facts as I could surmise, combined with my own experiences when I was her age (1999) and the teenage children of friends of mine over the years.
And after doing that? The actions taken are justified. She needed to be publicly ridiculed (and lets not forget that the entire world was not the target, just her friends - and respective parents - in addition to his friends as well), she's 15 and simply confiscating doesn't work at that age and will very soon be mixing almost exclusively with adults, with consequences far more severe than having a full clip be fired into her laptop. That her dad had spent 6 hours of his life upgrading and setting it up just right.
That last point will be lost on those who've never had to spend so much time fixing up a laptop, those of us who have will understand completely and wouldn't have needed as much reason to shoot the damned thing!
So far then, to answer the OP's question, I'm on the Dad's side. The only parts I'd be on the daughter's side would be in finding work that would be legal for her to do (hours wise!), only because its difficult for those 18+ to find work to sustain themselves; let alone someone who is 15! The world he speaks of (being a volunteer fireman, working two jobs, living alone and studying too) doesn't exist anymore. Indeed, the 16 year-olds of today - in the same or very similar circumstances to his 16 year-old self from back in the day - would find it far more difficult to find a place to live; to find one job (let alone two!); to afford to study and find the time to volunteer for anything. When he got to that bit, he just made me think of all the 40+ "already old in their heads" people who rant on about how "they did so much with so little and we managed!" which whilst good for them, is just not possible now.
But that's the only criticism I have as regards the Dad's attitude, I realise he was just trying to impress upon her how easy she has it but think back to when your parent(s) have said the same. Did you pay attention or just feel nauseous and mentally putting everything they're saying in the recycle bin? I'd bet money that's what the daughter was doing prior to this.
Go Dad! XD