Why is it dithered like this? To save bandwidth? I wasn't on the internet much before 2010, so maybe this is an old technique you don't see anymore.

Author answered below, but dithering techniques like these were common on old computers like the C64 and others, due to the limited ammount of graphics colors available ( 16 colors on C64 if I remember correctly), plus there were usually limitations on how many colors you could use within one 8x8 block , commonly 2 - 1 foreground , and one background color. C64 had a multicolor mode with 1 background, and 3 forground color. But that was still just 4 colors (out of 16 available ) usuable for each 8x8 character block. However switching to multicolor mode took you from high resolution ( 200x320 px) to low res ( 200x160 px) - and yes thats for the entire screen (25 x 40 chars)

Originally, sort of. But also to work around limitations in GIF (which is palette-based; but see https://en.wikipedia.org/wiki/GIF#True_color) and because people didn't always have true-colour monitors (or ran the monitor in a different mode due to VRAM restrictions) anyway.

In today's context, more for the aesthetic, presumably.

it seems obvious for nostalgic reasons