David's article suggests that his problem is that cooperative cultural interactions take place between organisms which "lack genetic relatedness, genealogical or otherwise". This seems like a basic point that is very easy to explain. Much cultural cooperation is based on shared memes. When two individuals have the same money, the same language or the same religion, they are more likely to cooperate. The more shared memes they have, the more likely they are to cooperate (on average). The idea of cultural kin selection is based on cultural evolution, kin selection acting on memes (rather than DNA genes) and symbiology and manipulation.
David says large spatial and temporal scales are part of the problem. I don't understand this problem. Consider the US dollar for example. This exists in billions of identical copies - and produces a lot of cooperation - which is all well explained by cultural kin selection - since the dollar bills are close relatives with r~=1 - and they clearly influence manipulate their hosts. The dollar's reach is global and it has lasted for quite a long time. It is not clear what the supposed problem with large spatial and temporal scales is.
To reiterate some by-now tired points, kin selection emphasizes close relatedness - where the process actually produces adaptations - such as the human breast. Group selection de-emphasizes relatedness. As a result advocates apply it to groups consisting largely of non-relatives - such as entire tribes - where theory predicts that the process is largely ineffective. As a result group selection has a long (and ongoing) association with junk science.
Mixing cultural evolution and group selection is a recipe for confusion. That's the very last thing the important science of cultural evolution needs. Mixing the two is not helping to educate the public, it seems more like a controversy-based marketing strategy. To me it looks like self-promotion at the expense of misinformation.
To reiterate, it is not the case that group selection explains cultural dynamics that kin selection does not. Group selection enthusiasts have spent decades looking for such cases. They have failed - and now most of them have given up. I thought David Sloane Wilson was among those who had publicly thrown in the towel - and given up this quest. This article suggests that the old group selection dream of finding new science and making original predictions still lives on. That does not seem like a good thing.