This resonates so much with me and my kids. On Saturday when school is out, they'll spend 80+% of their day engaging with one screen or another. And during my non-work time, blogs and forums (ahem), online news and magazines are where I end up spending a lot of time...
Maybe your family should try what the person in the video has, a weekly "non-screen" day where everyone turns off their cellphones, computers, and TVs. Your kids might object at first, but it will be good for them in the long run.
Wouldn't that just open up the family to be 'distracted' by something else? If the family wants social time, yes, there should be a social time set up for games or mutual activity, but otherwise it will just open up for kids to be distracted with books. I've heard very social parents complain that their kids rather read than go play with other kids (and been complaint since books/learning has been around). I knit to keep my hands busy when watching anything or in church listening.