Kids watch adults to learn the adult behaviors that lead to safety, community, and procreative success. If the only lesson they ever learn is that their behavior when bored is the center of the universe, they are going to have a hard time as adults.
Around your children, you should behave in a way that is reasonable and ethical and safe for an adult to behave. You should also make it your first and highest priority that they don't die. If you do those things, then go ahead and play with your smartphone.
Chances are, when your kids grow up, they will find work, friends, information, and entertainment valuable as well. There is no harm in teaching them that you value those things too.
Which is exactly what the author's saying. "Nothing on any screen is more important than the time I spend with my kid." When he's spending time with his kid, all other things are secondary. When he's not, other things are okay.
As a father of three, I've learned it's okay to drift after playing Candyland for the 10th time. It's called being human. Your child isn't some precious stone you need to admire 24 hours a day - it's okay to live your life too. And you're in trouble if they begin to feel it's your job to entertain them every minute of the day.