This article seems to assume that changes in family structures are a cause of men not working. I see no mention that it could actually be an effect of that. Who's gonna want to marry (let alone have kids with) a man who is unemployed and isn't even looking for work?
This betrays your unfamiliarity with the segment of population under question. As it turns out, lots of women will readily have kids with those men. Along with the growth of single-man household, we observe growth of single never married women with children.
See for example "Promises I Can Keep" (https://www.amazon.com/Promises-Can-Keep-Motherhood-Marriage...) and "Doing the Best I Can" (https://www.amazon.com/Doing-Best-Can-Fatherhood-Inner/dp/05...) for some sociological view of realities about the lives of people this discussion revolves around.
That is to say, it is not entirely clear that an apathy problem among old men is the cause of declining marriage rates, given that most people marry well before the age of the men in the article.