If overall productivity growth is low, we're not seeing an increase in unemployed people due to rising productivity. So it's not "yay productivity (though it is generally a good thing)," it's "productivity growth at a level that is noticeably affecting unemployment isn't happening." The whole discussion about the impact of technology of job demand centers around the belief that productivity will suddenly and sharply reverse course (or more likely, around people not being aware that productivity growth has always caused job displacement and that that effect is shrinking).
Longer quote:
"This means each additional robot added in manufacturing replaced about 3.3 workers nationally, on average.
That increased use of robots in the workplace also lowered wages by roughly 0.4 percent during the same time period."
Looks to me like that's referring to manufacturing. The longer piece also notes that the *slowdown* of productivity growth has caused a drop in labor demand.
We do know that male prime-age LFP has been declining since at least the late '40s. We don't know that that's caused by increasing productivity. It's likely that automation has contributed to it, but there's a lot more going on here, and I don't think that anyone has a good answer. Note that about half of prime-age men not in the labor force are disabled. We've also seen rising incarceration rates during the period. It's a very small part of it, but an increase in house husbands is another factor. Globalization is often blamed here, and while I think that's overblown (just as the technological explanation is), it could be a factor. Another factor is a shift in the composition (that is, we're looking at 25-54-year-olds, but over the period, the distribution within that range has shifted, which could also be a factor in the disability rates). Another one is that we haven't done a great job of recovering fully from recession to recession. Anyway, there's not a lot of room in the numbers for a big effect, as you have a lot of factors that plausibly make a difference and a total effect that isn't that big.