I'm a librarian who loves anime, manga, and reading a wide variety of genres.
"The word they used--or the concept, at any rate, as I understood they didn't speak in words--was usually translated as significance. And only the Presger were significant."
This is maybe an error, unless I have the timeline wrong. I had thought that the Presger had treaties with both the Geck and the Rrrr prior to their treaty with Anaander and all humans. That would mean that the Geck and the Rrrr were both considered significant by the Presger by this point in the book.
Also, hurray for my being able to follow the politics this time around!