Yeah, that's the joke he makes in the video.

What you're asking is like proof that I've made this comment, you don't need me to show you that I wrote it because the evidence is automatic based on your ability to comprehend what I'm saying.

Jordan Peterson makes conclusions based on evidence and then uses them to argue his points. The proof is you just need to observe the facts he uses (and I'm being generous here, assuming the data isn't taken out of context or something) and then listen to his arguments to discern when he's using what the data suggests to explain his point versus when he's using the conclusion he drew from the data to explain his point.

I think you'll find it's more often the latter than you initially realized, the man is good at talking in circles both because it makes it difficult to call him out on his bullshit as well as providing an air of expertise and intelligence.