No this guy actually understands what he’s talking about. He may not be articulating it the best, but his argument is not false. What he’s essentially saying is that based on what we understand now, the brain must be a machine in some sense that can do computations.
The only reason this is the case is because logically unless new physics arises this must be the case. So it’s not the brain is a computer like we have now, it’s that all things that process and handle information systematically must do computation. What that looks like and what each unit does it what we don’t get.
I have a reply to most of the points you’ve brought up which I hope will help you see another perspective. Some things I hadn’t even thought of until you wrote this (thanks). But I don’t have time to write them all now, nor do I want to type it all out at my phone. Leaving this comment as a reminder.