This is a fascinating article. I'm not a linguist, but was able to follow their arguments.

My (admitted non-practitioner) criticism is that their analysis looks at the corpus of only one writer. They pick up significant differences in language use between true articles and articles where it is known the writer was intending to deceive. What's not clear is whether this difference is larger or smaller than the obvious differences in language use between authors. If smaller, their technique is only useful for analyzing the body of work of an individual, but isn't that useful for checking whether texts from a different author are deceptive.