Back then, they even had a low-bandwidth version of the site: http://web.archive.org/web/19990117023050/http://www.nytimes...
The website included various tutorials on how to use it, including a guide that covers the different browsers. None of the browsers listed are actively developed today: http://web.archive.org/web/19961112182937/http://www.nytimes...
edit: A couple of other observations:
- How many other content websites have published for nearly this long and yet have their oldest articles remain on their original URLs? Most news sites can't even do a redesign without breaking all of their old article URLs.
- I like this Spiderbites feature -- a sitemap of a year's worth of articles (likely for webcrawlers at the time): http://spiderbites.nytimes.com/free_1996/