Not sure if it is what was used, but there is a Bill Atkinson dither for HTML canvas here https://ipenburg.home.xs4all.nl/atkinsome/ and a mac version here https://www.tinrocket.com/content/hyperdither/#history
https://github.com/ipenburg/Atkinsome
The script is about 8 years old and depends on MooTools, but shouldn't be too hard to modernize it.
Here's a newer implementation of the Atkinson dither algorithm on Node.js.
https://github.com/rtrvrtg/node-atkinson-dither
Edit: This dither library includes Atkinson: