*This is not to say that women don't play sports with their sons, but to say that it's silly to assume that all young fathers play sports with their sons.
True but I'd bet that many of these men came from urban areas where the community had services in place for younger people to find older mentors, and generally stay out of trouble.
I'm from eastern Kentucky originally and was lucky to have a fantastic stepfather, but I watched a lot of kids grow up with not much support past their single parent of either gender, and only a few of those I knew made it to 18 going anywhere near the correct trajectory. Outside of churches, there wasn't a lot of taxpayer-funded support for kids with single parents as it was probably a "moral" issue to the local politicians who still find the idea of a single parent family abhorrent and prefer to ignore it.
In families with older fathers, [assuming] there is a higher percentage of dual parenting ... which could mean more attention at home = less time playing sports with the neighborhood kids