Don't get me wrong, I dig the retro art style, but at that resolution, dithering gets in the way of legibility. I think for the chess pieces themselves it makes more sense to trade off some of the realism (i.e., shading, specular) to better communicate the shapes, particularly as it's so important to game play
I'm aware of that composite signals tended to bleed pixels horizontally. I used to draw my own pixel art when I owned an Amiga (though to be fair, the monitors were often sharper, and I wasn't always using composite). I grant perhaps it's more legible on a composite display, though I think that's a hard thing to appreciate when delivered on the modern web.