What's happening here is that Google wants to spy on which links you click and track your activity on that site by explicitly setting new cookies in the link's new tab from the URL params (re-bootstrapping a tracking cookie/etc to defeat opening it in an isolated tab or private browsing window), so they rewrite all links to point to their redirector endpoint.Such an endpoint is vulnerable to "open redirect" exploits, where a redirect exploit on a trusted domain (google.com/youtube.com) is used to conceal a malicious link. The confirmation page is used to make the endpoint useless for such purposes.
But the confirmation page would be super annoying for normal users who intended to click the link, so there's a further mechanism where the redirector link has some ID that's also present in your cookies, so that as long as it is you who hits the redirector endpoint the confirmation page is bypassed - but if you try to use it in an "open redirect" attack your victim wouldn't have the matching cookie and thus would get the warning.
In their case they must be opening the link in a new context that doesn't share state (cookies/etc) with the old one (either deliberately or as a result of a privacy plug-in/feature) and so get the interstitial.