There's probably a lot of complicated ways of doing this, but to keep it simple you could probably just downscale the image, convert to black and white, and have an array which maps lightness ranges to ascii characters
Looking at the source, looks like he piped it through http://secret-wildwood-1014.herokuapp.com/, which looks like it does basic image to ascii conversions when you give it a url. Not sure if he spun that up, but it's cool in that now the app can be made all in js
I wrote a program for playing video in ASCII on an OpenVMS console (VT220 orange text serial console) for a university project.
I played the Matrix dojo fight scene for the final presentation, it was a big success! :)