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.

It's an archive page, but that's pretty much what the website looked like in 1999:

https://web.archive.org/web/20171230005844/http://www.nytime...

https://web.archive.org/web/19990209200635/http://www7.nytim...

That's definitely 1999-era HTML and layout, except for the "This is an archived page" header, which is the only CSS on the page.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.

Regardless, I wish I could get this version of the website for current articles.

That seems to be a common theme with websites. Not to mention how quickly it loads...

back then I was probably still on my brand spanking new awesome US Robotics 56k modem!

Does it? Each line of text spans my whole monitor, which doesn't make for a very comfortable reading experience.

Back then it would have been fine since the monitors were small and square.

You don't have to have your browser spanning the entire monitor.