To be fair, applying a bunch of filters in GIMP or another image editing tool could get you 90% of the way there (Adjust HSV -> Downsize with nearest neighbor interpolation -> Posterize -> …).
My sample above was done using nearest neighbor downsampling, converting to indexed color in Photoshop, changing the palette size to 8, then adjusting the palette indexes by hand to pump up the saturation and contrast. Of course, for really gorgeous pixel art I'd have want to do a ton of pixel-by-pixel hand edits to make it look just right--That's where 90% of the effort goes, even if visually, yeah, the purely mechanical stuff is what makes it recognizably pixel art.
See, what I'd really love is a workflow to convert art to indexed color in such a way that the palettes are truly interchangeable like in the old SNES game--maybe to 16 colors, with transparent, your darkest color, your lightest, two series of six in-between values representing two different hue and saturation curves between them, and a spot color. Figuring out an algorithm to cluster an image's color space around the appropriate values sounds like a real pain, though.
Thank you!