Much of the paper is devoted to showing that monogamy is good for society-level fitness. They invoke cultural group selection to explain monogamy's spread.
Slavery seems like a suitable point of comparison. This is also widely banned - despite the fact that the richest might be expected to benefit most from it.
Wife inequality is seen as more of a moral issue than wealth inequality - and technological growth independently fuels wealth inequality.
Is the spread of spread of monogamy down to cultural group selection? I'm sceptical. It is true that in the democractic, religious and political revolutions and invasions that have spread monogamy a whole buch of memes gets supressed at once. However, describing this as being a form of group selection seems a bit controversial. A whole bunch of birds went extinct at once when mammals reached New Zealand. However, few would describe that as being a form of group selection. The invading animals wiped out the natives bacause they were fitter than them - not because of group-level effects.
Looking at large groups of memes going extinct during a major mass extinction event isn't terribly good evidence for cultural group selection, IMHO. In general, one group of organisms systematically wiping out their neighbours is just evolution as usual. Group selection - at least of the type that is controversial among biologists - is a more demanding concept than this.
The outcome shows that the monogamy meme bacame fitter as civilization progressed. If it could additional be shown that monogamy lost out to polygamy within groups, that would then qualify as evidence for group-level selection. However, the paper doesn't do that, and the idea that the polygamy meme wins within groups is probably simply false. In which case, group selection is not clearly needed as a hypothesis to explain the results.
A simple explanation for monogamy is democracy. Monogamy is deleterious for 90% of males and probably most females too. The few males it benefits may be powerful, but they are simply out-flanked by the rest of society. This explanation is simple, obvious - and it doesn't invoke group selection.
Memetic altruism is the most obvious thing to look for if looking for evidence favouring cultural group selection. At the moment, people see things that aren't explained by existing theories of altruism, and then invoke forms of group selection. However, it seems to be that this happens largely because they don't have a decent list of the known causes of human altruism. That seems to be largely because of a widespread incomplete understanding of memetics. Account properly for the existing known causes of altruism and group selection theories have a lot less work to do.
Update 2012-01-31: Razib Khan is sceptical about the group selection too.