The story isn't really about "higher education" in the traditional meaning. It's about taking the blue-collar apprenticeship & training model and calling _that_ a "college degree". Since blue collar schooling (apprenticeships) and blue collar careers (e.g. factory workers) have a social stigma, some folks in the article are saying "degree required" should be expanded to mean "apprenticeship required". The last sentence of the article highlights this re-labeling:

>“And whatever you do with training, you need to call it college. You want to make people feel good about the path they choose.”

Other sentences in that article on that same theme:

> But the college-for-all movement, [...], is often conflated with earning a bachelor’s degree.

> “Higher ed,” he said, “needs to respect the dignity of labor.”

E.g. the prospective factory worker attends training at a community college for 2 years and gets a credential that's not a traditional bachelor's degree -- maybe a Completion Certificate and call _that_ the "college degree required". That's the idiosyncratic meaning of "Degree Required" specific to the NYT article's title.