The link provided with the title of the post isn’t necessary to click. I only put it there to provide a little bit of legitimacy to the post. It’s the NYT’s own domain hosting a page that provides the onion service and some info about it.
If you have Tor installed on your machine, you can copy/paste the onion at the end of the post into Tor’s address bar once you’re connected to Tor. This should navigate directly to the NYT’s front page. Note, if you’re part of the uninitiated, you must use Tor to navigate to the link. You shouldn’t see the page I linked with the post.
Even on Tor, if you use the clear web site provided in the link, yes, you will see the box asking for a subscription. You can click the x to get rid of it.