I think the article itself is disappointingly shallow, but it touches on an important issue worthy of discussion.

My understanding is that a large part of this comes down to two things. First, how the parents value education and model the value of education to their children. That is, they are encouraging their children to learn and to do well at school, not just by telling them "you have to do well at school", but by little things, like not belittling the scientists on TV because they "don't live in the real world", or by turning up to their child's school events and displaying enthusiasm for their efforts.

And second, by how the parents act as educators for their children. Things as small as reading to your children before bedtime have been shown to have an enormous benefit to their reading ability. Or spending time with them playing games with educational value that help them enjoy learning. I remember as a young child really liking the old Who Wants to Be a Millionaire?, and my dad would play "maths Who Wants to Be a Millionaire" with me. Literally just a multichoice maths question, but by framing it around a show we watched I got more into it.

Both of these factors can be difficult for people of lower socioeconomic status to do, because if you're busy spending all your time at work just to make ends meet it doesn't leave a lot of time for play with your child, or to go to their events on a school day. And many parents probably just don't know the value of these things or how to do them in such a way as to get the best outcome for their child. And of course if your parents didn't do those things, you probably just internally think of it as normal not to do those things, because so much of what we do is modelled after our parents. So it's a difficult problem to solve, but it's one we need to really acknowledge as a society before we can even begin to solve it.