> Is it simply that humans have about 30k genes, your children each only get half of your genes, and so after about 16 generations it is possible for someone to be a descendant of yours but not have any genes that came from you?

Yes, the difference between genealogical ancestry and genetic ancestry is just the reason. The modelling which gives those estimates for the IAP assumes very infrequent migrations of individuals – one per generation is enough. That level of migration would likely leave no genetic heritage at all. Probably many Africans have literally zero genetic inheritance from Neanderthals, but almost certainly those same Africans have Neanderthals in their ancestor tree, albeit through only a few lines of descent.