That's a scan of the printed version. You can look at the front page (nytimes.com) for free, but you need a subscription if you want to read more free articles than a limit allocated to non-subscribers. "Paywalled" means you can't read the full article, it's hidden or truncated.

The front page of the printed edition has 5 full paragraphs.

The web version shows a headline and one sentence.

Those are links to articles, not the full articles themselves. Similar to the "continued on page x" in the printed version, you will need to go to the full article to read its contents.