He isn't saying the purpose of peer review is to replicate work. And yes I've personally reviewed quite a lot of papers (from outside of academia), also occasionally reviewed peer reviews.

What he is saying is that peer review is treated by academia as a close to gold standard, when it's really more like a bronze standard. It's a bit like finding a software company that exclusively uses volunteer post-commit code review with no unit tests or static typing, and in which the only testing process is to push to production and see if anyone inside the company complains.

It's not useless as a concept, and it's generally better to have a paper that's reviewed than one that isn't unless the field has been captured by ideologues. But there are so many common problems it can't fix, not even in principle.