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Why do you expect anyone would pay for this article, when the NYT website is currently free with unlimited access?

That's what the 'web' link is for. It takes you to a Google search for the article. Click the top hit to bypass the paywall.

even if you do click on web and hit the first result, you still get a paywall.. maybe it's a US-only thing?

Works for me (and I'm in Europe)

I get a paywall through the web link (from UK).

However right-clicking the main link and opening in private browsing seems to work.

This gets asked and answered so often than perhaps HN should add an instruction to the "web" link that tells you to open it in a new private/incognito window.

From the FAQ:

Are paywalls ok?

It's ok to post stories from sites with paywalls that have workarounds.

In comments, it's ok to ask how to read an article and to help other users do so. But please don't post complaints about paywalls. Those are off topic.

Either clear cookies, install an extension that clears cookies, or open the "web" link in an incognito browser session and open the Google link from that.

At least one of those options should work, most likely all three will.