Thank for digging up the article!
The guessing can continue, but the authors and the data in their small study says it pretty clearly: It's the income, guys!
There seems to be no proof that it matters that much, although I suspect that managing screen addiction becomes important at later ages. It's possible that letting kids have some screen time at younger ages, and teaching them from the get-go about the dangers of over-consumption/addiction, could end up being a very valuable parenting technique in the long run.
Obviously the example you gave makes intuitive sense, but there doesn’t seem to be any research or other evidence to support it at this time.
Also, yes, there is a tie between income, education and culture, and it goes both ways. Starting one's life around cultured and educated people does help you grow into someone who has access to a better job, which gives you access to better education and culture, etc.