In fact, even in the 80's, dithered images were often larger than their un-dithered counterpart, sometimes by a lot. But it was worth the trade-off when the alternative was an image with so much banding that it could be confused for a European flag.
Unless you're trying to display your image on a retro console (or have aesthetic reasons for wanting to achieve that effect), you should not use dithering. Essentially all modern devices have a sufficiently enormous color palette, and modern compression algorithms use other techniques to achieve their efficiency.
In fact, modern compression will do a much better job giving you a smaller file size if you don't use dithering.
Edit:
Don't get me wrong, dithering is a super interesting topic, and designing a good dither can be surprisingly hard, it's just not going to help you if your goal is to shrink the images on your website the way the article claims.
If you haven't seen the trailer for "Return of the Obra Dinn" you owe it to yourself to take a look:
Super cool aesthetic, and writing that shader must have been all sorts of difficult/fun. But you don't do this sort of thing for compression efficiency.