https://www.bls.gov/news.release/empsit.nr0.htm
and the numbers:
https://www.bls.gov/news.release/empsit.t01.htm
It's actually kinda straightforward, and very clear about what measures they're using. The numbers are bit scary - "The employment-population ratio, at 56.6 percent, changed little over the month but is 4.5 percentage points lower than in February."
"The number of persons not in the labor force who currently want a job, at 7.2 million, changed little in September; this measure is 2.3 million higher than in February. These individuals were not counted as unemployed because they were not actively looking for work during the last 4 weeks or were unavailable to take a job."
So that's 12m officially unemployed, plus 7m "not in the labor force" but who want a job.
So yeah, the article is kinda on point; that the numbers don't mean what they think we mean. But I have to agree: that's not because the numbers aren't available for anyone to look at and understand.