There are some considerable weaknesses in concluding causation here. Their theory is a sound proposal, but countries with higher levels of health, also are wealthier, more socialist, and other factors. All of which might be relevant.
One possible confounding variable that immediately lept to my mind was a study published sometime in the past couple years indicated that women's preferences change depending on whether they are currently taking hormonal birth control. I believe it did say that more "feminine" characteristics were more attractive when taking such birth control - and these birth control methods are probably more common in countries with better medical systems in general.
They quote Romania as one of the low-masculinity countries while Bulgaria as one of the high, so as somewhat polar opposites. There are very small differences in terms of wealth, health care access, or even physical location between these two countries.
I'd be interested to know what effect the womens rating on masculinity had to do with what position they where in their own life, sexually and socially.
From what I've read of evolutionary pyschology, when women are younger and adventurous, or when their friends are single, they are looking for alpha males. But when they want to settle down they often lean towards less masculine beta males.
dominant strategy is sleeping with alphas and keeping a beta for resources/security. cuckholdry rates being far higher than is generally assumed seems to support this. avoided topic because it makes people uncomfortable.
Author misses an important point. Evolution by sexual selection only applies to a woman's choices 3-5 days out of the month, when she is able to conceive and become pregnant. Any study that doesn't take this into account is going to get some misleading data - a woman's preference in men the non-conceiving 25 to 28 days out of a month has a lot less bearing on evolution and sexual selection than the other 3 to 5 days.