Good article. But it's not an argument against essentialism. If two states are judged to share the same emotional character, then they necessarily have something identifiable in common, namely, an essential property. The author merely wants a better measuring device to find this essential property, not to abandon the search.
Darwin did update the idea of essences by giving us many more to work with. The finding of transitional forms in the fossil record helped drive this point home. He also showed that whatever their center of "essential mass" was, it definitely wasn't immutable as many had speculated before him. By explaining speciation through gradual change, Darwin showed us that every species' core is in flux.
For John Dewey (who famously wrote about the impact of Darwin on philosophy), this meant that the concept of a fixed and eternal essence in biology was then metaphysical baggage. But Dewey jumped the gun a bit because he was writing before any understanding of genes. Nowadays, genetic essentialism is an indispensable notion in biology, since it is mostly only by sharing in some genetic core of what a species is that enables two tokens of that species type to interbreed productively.
As for the article, I gather that one of the author's primary aims was to discredit the theoretical basis of practices like profiling, lie-detection, and such. She also wanted to show that localizing emotions in one part of the brain is a fool's errand, which she did to great effect. And while her point about the statistical nature of reading each other's emotions is valid, it's certainly not a stroke against the idea that all feeling states of one kind have something in common. After all, if they didn't, then we'd constantly be unsure whether it's hunger or xenophobia we feel when we smell pancakes in the morning.