I always zoom in on pictures on the web to see if the compression is good or if there are artifacts.
I agree, it's not a good example to lead with.
That said, in the context of showing off your photography I can understand considering these kind of artifacts undesirable, even though they're perfectly fine for a lot of other uses. On my own website I spent quite some time downgrading my mugshot to be as small as possible without too many artifacts – it's now 4.9K in WebP, vs. 9.2K in JPEG before. Maybe that was a tad obsessive though...
I do think the author doesn't quite appreciate that most people are not photographers, and that for most images quality doesn't actually matter all that much.
It's not so easy to see if the browser zooms the image, so make sure to open the image and set zoom to 100%. I also need to keep my face fairly close to my screen (12" 1920×1080, so not that large).