The dithered example is a bit disingenuous, since it coaxes the picture into a palette that is clearly not suitable, causing an egregious amount of artifacting.
I don't know what's going on with their dithered image sample:
Further, human eyes are kind of bad at blue colors, so whatever compression artifacts you get with JPEG or WebP is going to be really hard to detect. (The blue channel is typically compressed much harder by many algorithms because of this).
