I checked out the actual study. The mean times to complete a four-piece puzzle representing a horse (their measure of 'spatial ability') was:

• Patrilineal Males: 42.31s
• Patrilineal Females: 57.2s
• Matrilineal Males: 32.1s
• Matrilineal Females: 35.4s

The difference between societies is strongly significant: the matrilineal society was significantly better at completing the puzzle. The sex difference in the patrilineal society is significant. The sex difference in the matrilineal society has a p-value of .025: that is, significant at the 5% level but not at the 1% level. In the matrilineal society, education was equal across genders, which explains a third of how much the gap closed (as education favored males in the patrilineal society).

The medians, though, are screwy:

• Patrilineal Males: 32.5s
• Patrilineal Females: 42s
• Matrilineal Males: 27s
• Matrilineal Females: 20s

As expected, the mean is larger than the median for every group. The median female in the matrilineal society, however, finished far faster than the median male in the matrilineal society- despite the males having a faster mean overall. The times overall appear lognormally distributed, but they don't provide the distributions for each response group. I'd like to take a look at the matrilineal ones and figure out why the median relationship doesn't align with the mean relationship.

A couple of comments spread throughout the study suggest that this result should be seen as abnormal / barely update your probabilities. (Among other things, they point out that every other study shows no significant link between gender egalitarianism and spatial ability, and so this study is significant as the first one that shows something like that.)