Hardly anyone is writing their styles to set the body text to Times New Roman. Aside from serif typefaces not actually being so bad, if you're seeing Times New Roman on sites like these, it's because you haven't set your default font and your browser is falling back to it on your system.

Fixing this in Firefox is as easy as opening about:preferences in a new window and selecting your preferred sans font. Dan's site will instantly be transformed, and every other site like his (e.g. http://cr.yp.to/ https://motherfuckingwebsite.com etc) will be rendered similarly for all future visits.