From looking at the source, there's just the regular jQuery and Underscore libraries, and a bunch of custom JS, including the jQuery Waypoints library http://imakewebthings.com/jquery-waypoints/

The animated graphics are SVGs.

Mostly though, this is just a lot of hard work writing custom HTML/CSS/JS.

From what I've heard from The Vergecast (sister publication), they have a custom CMS that focuses heavily one building these super-custom one-off designs for 'big' articles

Yep, done in Ruby on Rails (well, at least all of The Verge and Polygon is) IIRC.

It's done by updating stroke-dasharray, stroke-dashoffset.

http://bl.ocks.org/mbostock/5649592

http://jakearchibald.com/2013/animated-line-drawing-svg/

But it's not that new as one would think.

http://www.carto.net/svg/samples/animated_bustrack.shtml (2008)