The way this article is written, saying "tech boss" implies de-facto boss of the home and the child's behavior, is flat and silly.

Both parents are bosses of the home.

If one parent does not co-operate to limit social media — it's unlimited by default for the kid.

No, in this context, "tech boss" refers to parents who are also executives of technology companies.

I agree with the point you make in the rest of your post, but it feels not really relevant given your misunderstanding?