In other words, they get to 1% of the filesize by reducing the number of pixels to 2.5% of the original count. Once you've done that, you can get a better looking image by using Squoosh than by dithering.
https://imgur.com/a/9bGGA4j shows a comparison of the original, my squooshed version resized to the same dimensions they used (at only 41 thousand bytes), and their 65 thousand byte dithered and resized version.
Their version, 160% the filesize of mine, is much worse, obliterating detail of the clouds, for example, and also being ugly. Unless deliberate dithered ugliness is your stylistic choice, you should not be dithering unpaletted filetypes like jpegs. I'm not saying my version is perfect; I would never compress a jpeg so heavily that the block pattern shows (as it does in the upper left clouds), but where that is apparent my competition had simply deleted that information completely.
> There may be other compression mis-choices on the original JPEG as well.
You bet. I also include a highly compressed version of the original image, which comes in at only 394 thousand bytes, not 6176 thousand like their totally unoptimized one, which is a 94% savings all in itself. I chose to compress to the point that the detail of the men on the large barge mass was without apparently loss of quality. Again, this results in visible compression artifacts in low-contrast areas of the image, like the water surface and clouds. From my experimenting, settling for a 1500 thousand byte image results in a dssim score of very nearly zero and would be what I would consider properly optimized, at a 75% savings.