1. People make sense of things through language. (You can get this sentiment in sound-bite form from any number of linguists or language philosophers, e.g. Wittgenstein's "The limits of my language mean the limits of my world.")
2. People with more linguistic resources are better able to make sense of things, and thus tend to rise to the top of the pecking order. (N.B.: Language is more than just words, so this isn't simply an issue of vocabulary.)
3. People with fewer linguistic resources are drawn to the expressions of people with more linguistic resources because those expressions give them new ways to make sense of things. They're like design patterns for thought.
4. Thus, what's being measured isn't power or influence, at least not directly.
But of course none of this is relevant to the article, which draws its conclusions from the degree of periphrasis in a discussion, rather than the substance of what is said. So, again, very interesting.