The paper didn't mention knot theory or dynamical topology because, like I mentioned, those are areas that my research bring into the picture, but was the result of (what I suspect) is the same end goal. I read through the author's blog and my jaw kind of dropped, it was uncanny how similar paths we went down. It's clear he's interested in a general theory of linguistics that can be described in the language of algebraic topology among other mathematical branches and theories, so information theory was obviously involved. However, he's way ahead of me in respect to the subject of the paper; most of my spare time has been dedicated to the greater evil, which is prime number theory, but that paper (although has proof of concept) is still far from polished but I know who's perfect now to review it when it's ready.
The answer at the end is that we get a derivation (Shannon Entropy) on the operad of simplices. What is the connection to knots and chaos?