These links will not open the iOS app from this page. They point at the same domain you are already on, and iOS deliberately keeps same-domain navigation inside Safari. That is correct behaviour, not a broken setup — so this page cannot be used to test iOS universal links. Put the URL in Notes or Messages and tap it there. Typing it into the address bar never works either.
On Android the same links are a valid test, provided the app's domain has verified. They are also what a visitor without the app sees, so they double as the web fallback.
This page is also the fallback: without the app installed, these URLs are just pages on a website. That is the point of using https rather than a custom scheme.