This idea is called
linguistic determinism or, more commonly, the "Sapir-Whorf Hypothesis." It's largely discredited nowadays, but there's been a lot of discussion about it, so there's a lot you can read about if you're interested.
It's discredited as a strict theory of cognition, but at the same time certainly true that language has a large impact on how we think and what we think about. Not in the form of grammar and whatnot, though wordplay is pervasive, rather in the concepts you possess and solidify through use of language, which language then represents. The scope of one's thoughts can be radically changed by learning a word and it's underlying concepts.
There is then the third layer that communication must occur in a reduced medium like speech, which relies on the assumption that those who hear you have a compatible concept backing the words they hear you say, so that they can construct your meaning from their own bricks out of the plan reduced to language. On the one hand you can't just hear a new word in isolation and in doing so possess it's concept; on the other hand the meaning of a word can be very specific or disputed.
In the chapter this is somewhat the role of the Key, it is a translation layer built between two people with the goal of performing this same task at a higher abstraction and fidelity without needing to render down so far.