I mean, his 12 points are pretty stock Stoicism, with a 21st century spin. By my reading, he's not entirely stoicism, true, but he sits in the adjacent seat. If he is this popular with (as I see it) his re-skinned stoicism, then the conclusion that 'stoicism needed an update' is not unreasonable, as it seems to resonate better with the re-skin than without. Caveats, obviously, apply.
No, it's not. Stoicism has much more depth and the Stoics would not agree with Peterson on many things. Stoicism also doesn't need to be updated.