This happens in Android too and it's a little annoying too. If the app is using a certain web view tech (Android has a few) then it enables a frame using your default browser and an option to "Open in (...)" which correctly pops open the YT app. If it's an older web view sometimes it's just impossible - sometimes a share action will work, other times there is a link on the page.

Sometimes I'm logged in (I guess one of those web views got logged into at one point) and then I can watch a few seconds, manually open the app, go into history and restart it proper.

Not fun.