The reductionism is the attempt to generalize incomplete biological understandings to the high level systems of which biology is the basis. This ignores the complex interactions and properties that emerge at various points between the two domains. It's as misguided as saying that computers aren't digital because the underlying electromagnetism is analog.
The article would be fine if it recognized that it was speaking in trends and generalities. But the information is presented as universal and individually applicable. For example:
> But a lot of women, in particular, find it hard to accept that they are still looking for a protector and a provider.
No doubt women find it hard to accept someone lecturing them on their preferences without allowing them any individuality.
The idea that searching for a protector is adaptive seems reasonable enough. The fallacy is thinking it must therefore apply unconditionally to every individual person and culture. Individual behavior does not always adhere to what is adaptive and there is no reason to think there aren't other adaptations that may interact with, override or invert this "provider seeking" behavior on an individual basis.
The diverse spectrum of human sexuality and romantic disposition is completely at odds with the simplistic view presented in the article. The system is too complex to understand in a few generalities.
> Part of understanding higher level cultural phenomena is understanding our biological interactions
I think It's more often part of an anti-understanding of higher level cultural phenomenon. My observation is that people who strongly believe in reducing love to chemicals or atoms are intellectualizing an area of their life where they do not feel capable, confident or in control. These beliefs then inhibit personal growth and an understanding of others. In the last couple of decades I have seen dozens of men and a handful of women grow out of reductionist beliefs.