The steadiness of this pattern over a half-century suggests that it's not about trade with China in the last couple of decades, or about specific recessions. Something deeper and steadier is going on. This decline in men in the workforce is concentrated in groups with lower skills, but Eberstadt points out that not all men with lower education levels are experiencing the decline. Instead, there are sharp differences in labor force participation among low-skilled men across geography, foreign- vs. native-born, and married vs. unmarried. He writes:

Modern America has witnessed increasing dispersion in state-level prime-age male labor-force participation rates since at least 1980. Moreover, major, enduring, and sometimes even widening gaps in prime-age male labor-force participation rates are evident for geographically adjoining states (compare, for example, Maine to New Hampshire, or West Virginia to Virginia or Maryland). ... [A] gap of roughly 25 percentage points separated the labor-force participation rates of foreign-born and native-born prime-age male high-school dropouts in 2015. Elsewhere I have shown that the gap in labor-force participation rates between married and never-married prime-age male high-school dropouts was on the order of 20 percentage points as of 2015. ... 

To my taste, Eberstadt underemphasizes the poor labor market prospects of low-skilled US workers; for example, his article does not include the word "wages." But he is focused instead on a different theme, which is that the long-term reduction in male participation in the labor force is also wrapped up changes in "family structure, government-benefit dependence, and mass incarceration and felonization." Of course, these factors are often intertwined and mutually reinforcing. Here's a flavor of his argument on each theme:

On the connection from marriage to workforce participation:

Even after controlling for age, ethnicity, and education, married men are decidedly more likely to be in the workforce than men who have never married. This "marriage effect" is so powerful that married prime-age male high-school dropouts generate labor-force participation rates in the same league as their never-married, college-graduate peers. ... Lest it go unsaid: The collapse of work for men in modern America is much more closely associated with family structure than race.

Many of the men who are out of the workforce are supported in substantial part either by government payments that come directly to them or that come to family members. Eberstadt notes further:

Available information, however, points to a number of troubling features about the world of prime-age male disability and non-work. Apart from the small fraction (around 13% in 2015) of prime-age male non-workers who are adult students, the remainder report spending many of their waking hours watching and playing on screens — over 2,000 hours per year on average. Almost half of these non-working men report taking pain medication on any given day (which should raise a red flag for those worried about the opioid crisis). And when we stratify by educational attainment, we find that around three-quarters of prime-age non-working men without a high-school diploma are reporting disability benefits, while over four-fifths report access to government health-program support. These facts taken together would perhaps be unexceptionable if we did not already know, thanks to journalist Sam Quinones and others, that the Medicaid and Medicare programs have been widely abused for opioid consumption.

On the issue of mass incarceration:

America incarcerates a larger share of its population than virtually any other country on earth. But the vast dimensions of mass felonization are little known to the public, mainly because, scandalously, the U.S. government simply does not collect data on this demographic characteristic of the national population. One signal study attempting to reconstruct the stock and flow of the U.S. felon population, however, estimated that, as of 2010, nearly 20 million adults in America had been convicted of at least one felony. A little bit of arithmetic would suggest that the current U.S. felon and ex-felon population is now on the order of 24 million — meaning that well over 20 million felons and ex-felons today are not behind bars. Since sentenced criminals are disproportionately male, this means that over one in eight adult men in the civilian non-institutional population (the pool from which labor-force statistics are drawn) has a felony in his background — and the ratio for prime-age men today is most likely even higher than this. ... The "felonization effect" in reducing post-war prime-age male labor-force participation rates has not yet been calculated, but it is clearly significant in quantitative terms.

For a more in-depth dive into these issues, including lower wages for low-skill workers, as well as links to marriage, government benefits, and incarceration, a useful starting point is a three-paper symposium in the Spring 2019 issue of the Journal of Economic Perspectives (where I labor in the fields as Managing Editor):

• "The Declining Labor Market Prospects of Less-Educated Men," by Ariel J. Binder and John Bound 
• "When Labor's Lost: Health, Family Life, Incarceration, and Education in a Time of Declining Economic Opportunity for Low-Skilled Men," by Courtney C. Coile and Mark G. Duggan
• "The Tenuous Attachments of Working-Class Men," by Kathryn Edin, Timothy Nelson, Andrew Cherlin, and Robert Francis

A version of this article first appeared on Conversable Economist.