To help out readers who encounter a paywall (I didn't), I'll quote two key paragraphs from the article kindly submitted here. First, not quite halfway down in the article,

"What happened in America then happened in Europe and Japan in the 1960s and 1970s, in South Korea in the 1980s, and is now happening the world over. Student numbers are growing faster than global GDP. So hungry is the world for higher education that enrolment is growing faster than purchases of that ultimate consumer good, the car (see chart 1). The global tertiary enrolment ratio—the proportion of the respective age cohort enrolled in university—increased from 14% to 32% in the two decades to 2012; the number of countries with an enrolment ratio of more than half went up from five to 54 over the period. Sub-Saharan Africa is the only part of the world where “massification” is not much in evidence yet."

So undergraduate higher education enrollment is becoming commonplace all over the world. That, in turn, means that young people possessing an undergraduate degree is now more and more commonplace, so the job market has begun regarding postgraduate degrees more and more.

From farther along in the article,

"As first degrees become standard, more people are getting postgraduate qualifications to stand out from the crowd. In both America and Britain, 14% of the adult workforce have a postgraduate degree; and despite the increase in supply, the postgraduate premium has increased in both America and Britain, especially since 2000. There was a time, points out Stephen Machin, professor of economics at University College London, when a postgraduate degree depressed wages; but that was when maths PhDs worked mainly in academia, not in the financial sector."

The article, by the way, is a "leader" (an editorial) leading into a special report section in which The Economist does more detailed reporting on the role of higher education around the world and its societal effects. A crucial question, which deserves more research, is to what degree attending higher education institutions actually provides education, making young people smarter and more capable, and to what degree it simply provides social signaling, distinguishing one job-seeker seeker who had wealth and leisure time to pursue a degree from another job-seeker who had fewer personal resources. It is not clear yet that postsecondary education adds as much value at the margins as primary education does. The clear development model contrast between east Asia and Africa is instructive about this issue: at independence, Zambia was more prosperous than Taiwan. Many African countries developed national universities and attempted to provide higher education to local elites as soon as they became independent. Many of the college graduates from those countries then became part of the brain drain of emigration to the West. Meanwhile, in east Asia the focus of national education policy was on broad access to good-quality primary and secondary education, and industrialization and transition to a post-industrial economy in those countries was built on a base of broad masses of literate, numerate workers. And, as today's article reports, in the end east Asia ended up with more young people in higher education than in Africa anyhow, but along the way everyone became at least minimally well educated. For the same number of dollars, it probably does a country more good to improve primary education for the many than to broaden access to higher education for the few.