That’s an archived/print-formatted design. It isn’t how the actual website looked in 1999 (CSS and the DOM weren’t advanced enough for those kinds of layouts then), unfortunately.
That's definitely 1999-era HTML and layout, except for the "This is an archived page" header, which is the only CSS on the page. The rest is all well-known tricks from the time: tables, image maps, a few embedded images. Heh, it even has the blockquote trick to pad the margins. Brings back some pretty horrid memories.
https://web.archive.org/web/20171230005844/http://www.nytime...
https://web.archive.org/web/19990209200635/http://www7.nytim...