It's a joke, a meme response to "games looked so bad back then" types of comments made about games built during the CRT era and played on modern "perfect pixel", so to say, monitors.
Also, yeah. The site was ugly, you're not missing or misunderstanding anything. It's pure nostalgia to those who experienced the web back then, a reminder of a simpler, more ideal time in the internet's life.
It's just a reference to how CRT-era games look better on CRT as the devs were working with CRTs in mind and taking advantage of their way of rendering images[1].
I don't think there is actually a noticeable difference for the website itself, CRT performs a sort of interpolation which is great for old games that accounted for it, but for content that is already high-enough in resolution there is not any improvement
It's not supposed to look like that.