The HN rules are that paywalled content can be posted only if it's trivially bypassable via a free tool. The NYTimes links work on fresh IP addresses as part of a free allowance for new readers, which is why the proxy-based archive website archive.today is able to get through. I'm not a big fan of this being allowed, but there is some thought to it at least, they aren't just allowing anything.
That’d be sensible reasoning IF the articles were already posted with a paywall-free url, but they are not, so as it stands these are essentially just ads.
It is a shame that the free tool of choice is a site that put a DDOS attack in its captcha. So my options are not read the article or... not read the article. Nice.