Around the 1:30 mark he says "there is no difference between [writing] and thinking." He says that to highlight the importance of teaching people to write. If you are cynical, as I am, you might think that universities do not spend much time teaching people to write simply because they do NOT want them to learn how to think critically. But never mind!
I had a couple of lucky things that helped me learn how to write. Apart from a lifetime of doing a lot of reading--I don't actually recall when and how I learned how to read, all I know is that when I first went to school in Grade One, I already knew how to read--one thing that helped a lot was my first year English course at university. We had to sit an exam that basically just tested whether we could write a simple essay or not. I passed so I was assigned to a literature course rather than a remedial course. The professor was head of graduate studies so a very competent person and we also were taught by his assistant, a grad student in English. There were fifteen people in the class!! I'm sure that never happens these days--first year English? Anyway, we were taught how to write a research essay and studied poetry both reading and writing it. Good course.
The other thing that helped my writing was getting into the habit of sending letters to the Globe and Mail when I lived in Canada. I would send about one a week and got perhaps one in four published! It is not that easy. You have to pick a topic of general interest and you have to very succinctly express an opinion that will also be of interest. I got so I could tell when I hit the nail on the head. Nowadays I read a lot of stuff on the Internet and I see that one of the main problems is that people do not know how to be concise and succinct. One of the best possible writing exercise is to try and express your point of view in as few words as possible.
But I have one observation about the Peterson quote (which also does duty as my headline). You can think in words, yes, of course, but you can also think in music. Music is a form, a very odd form to be sure, but a form nonetheless, of thought.
A philosophical friend of mine gave me a present many years ago of an Oxford Dictionary in which he had inscribed the comment "For when riffs threaten to replace ideas." He meant musical riffs. But of course, musical riffs or motifs or whatever, cannot replace ideas. But they are another form of thought.
When I am playing or listening to music, I am following a train of thought that is entirely (unless there are lyrics) non-verbal. There is a narrative, a logic, an expression there that is simply on another plane from verbal thought.
Let's have an example. This is the String Quartet No. 8 by Dmitri Shostakovich played by the Borodin Quartet: