They don't explicitly state it in the article that I can see, but the PICO-8 is 128x128, and it appears that their output images were constrained to that. Your dithered images appear to be much higher resolution. I'd be curious what dithering would look like at 128x128!

Dithering is used quite frequently in PICO-8 projects at the “native” (128x128) resolution. Here’s an example from a few years ago: https://www.lexaloffle.com/bbs/?pid=110273#p