Excerpts the discussion part of the paper.

However, the drop of the male Ne during the mid-Holocene corresponds to a change in the archaeological record characterized by the spread of Neolithic cultures, demographic changes, as well as shifts in social behavior. The temporal sequence of the male Ne decline patterns among continental regions is consistent with the archaeological evidence for the earlier spread of farming in the Near East, East Asia, and South Asia than in Europe. A change in social structures that increased male variance in offspring number may explain the results, especially if male reproductive success was at least partially culturally inherited.

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Likely, the effect we observe is due to a combination of culturally driven increased male variance in offspring number within demes and an increased male-specific variance among demes, perhaps enhanced by increased sex-biased migration patterns and male-specific cultural inheritance of fitness.

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Finally, the inferred mid-Holocene Ne dips may represent a genuine population collapse following the introduction of farming, as has been recently shown for Western Europe using summed radiocarbon date density through time.

The bottleneck is associated with a shift from egalitarian hunter gatherer societies to big scale organized farming societies with a rigid hierarchical structure and organized warfare. You should be careful about drawing any definite conclusions about exactly what may have caused it, however, if you think about the stories in the bible and the stories about Mohammed's conquests etc. that might give you an idea. Those were brutal times.

This is just one study however, and it appears to be a new technique that they are using. A problem with science journalism is that they tend to report about some new (often controversial) study that comes out as if that's the truth now. "This is what scientists found". You should never trust one single study however, even if it's a good one. It's important to know the rest of the literature on the subject as well. That's why as a layperson you should look at the consensus of the relevant experts and not at one single study. This study hasn't even been published in the paper journal yet, you should probably wait for the critique that other experts are going to have of it before you start drawing conclusions. The ftl neutrinos experiment comes to mind as an example of why.