When I click on the first link in iOS Safari I get sent to a search results page served by my (read: my parents’) ISP. That’s pretty disturbing.
The second link appears to work. It’s a page that says “It works!” but it’s not HTTPS so of course I have no way of knowing whether that’s the ISP playing tricks as well. ;)
Why is that disturbing? For me, the name doesn't resolve (http://pn/).
Assuming you are using your parents' ISP's default DNS servers, isn't it a safe, though less-than-desirable, result for the ISP to forward you to a search page when resolution fails?
Using a different DNS server not provided by the ISP would most likely solve the problem.
You can do so in either the router or your computer/phone. Two well known and performant public DNS servers are found at 1.1.1.1 (CloudFlare) and 8.8.8.8 (Google).
It’s just a TLD that actually resolves; Most don’t. For example, http://com./ doesn’t resolve even though it has “subdomains”.
This does though beg the question: can a second level domain (root website) have (what we call) subdomains and not resolve itself? For example, example.example.com would resolve, but example.com wouldn’t?
I'm pretty sure that at one point I had to supply the trailing dot to make the browser (or resolver) believe it was a real hostname.