One thing I noticed in watching this is that JoPe didn't seem to have any awareness of different interpretations or schools of Marxism or his intellectual successors.
Usually a good sign for that is when a person seems to want to blame Marx, personally, for everything. When the real world criminals like Lenin, Stalin, Mao, etc. all did their own accurate discovery of the scientific principles of TRUE Marxism. If you can't even recognize this difference with huge figures of history, you'll never get to the internecine academic Marxist wars...
Even if Peterson had bothered to read the very good historiography that's attached to Penguin Books' version of The Manifesto he would have realized that Engels rewrote tons of stuff including translations of The Manifesto
in Marx's name after he was long dead. I have to imagine from the fact that Peterson is a tenured and apparently once respected PhD, this would have set off alarm bells no matter how far away from his field he's going. Even if he was being too lazy to read anything else but The Manifesto. Or even apparently wiki The Manifesto. (So perhaps I am being fantastical in imaging him reading a book.)
One thing I personally like to emphasize when teaching The Manifesto is how it was written
in response to political events, namely the wave of 1848 Revolutions. Both Marx and Engels wanted to get it out and read, they would finesse any details or theory later. It's almost irresponsible* to treat the work as standing alone and disconnected from these events.
*in the historian/academic parlance of "not actually important" except to nerds