Has the default font on that site been changed? IIRC it was Valkyrie, but now Century Supra is selected for me, and it doesn't seem to elicit quite the same breath-taking effect. (Not talking about Times New Roman on the linked page.) If my memory and senses don't fault me in the tiredness and drunkenness, then switching to Valkyrie (at the bottom) is highly advised, as with it this site is the most beautiful on the whole web. Every single interval is perfect, which causes fits of irremediable envy for me.
However, Firefox Preview on my phone doesn't seem to answer my efforts towards the aesthetic bliss and refuses to load the font.
BTW, my personal favorite free serif font is Merriweather—particularly for reading long texts. It's somewhat overused on the web, but it's so much better than the next thing. It has the exact right ‘density’, and the shapes are playful just enough to not tire out the eye.
As for sans-serif, alas! If I could have Rosario with good kerning and support for more languages, or Optima with a bit less contrast and more humanistic shapes—I'd be so happy. Until then, it's back to Fira Sans again and again.