Sometimes its really depressing neither to be really young anymore, but not being old enough to have seen the "old" Internet, when people still used html and only few companies had a website, therefore only few design-nags found there way into the web, trying to use it as some platform they can use to produce "art".
The question what exactly art is cannot be answered trivially, and I cant even give a proper definition of what I myself consider being art, especially as opposed to normal "work". Art doesnt need to serve a purpose and doesnt need to be useful, but it can be. Most of art wants to be consumed by a special kind of people - but not all of it. Well, lets stop this discussion here.
Something that most people should agree is how art works in the real life: People have material to work with - to rearrange, to use to rearrange something else, to compile. A sculptor gets stones and makes a sculpture out of it. A painter gets a canvas and colors and makes a picture out of it. They use some mateiral they have and arrange it in a way people consider valuable in some way. Especially, this material cannot be changed trivially in most cases. A stone has to be taken as it is, and sculptors seldom use concrete for their artwork - plasterers do, but thats another form of artwork, they form their sculptures before the concrete dries hard.
It is an essential part of art to have something given which cannot be changed trivially. And here comes the difference to modern web design. There are basics given - HTML, CSS. If somebody uses these elements to create a website that looks good, I could talk about calling that art.
But then, I often see JS and browser-specific code to make a website "look good in all browsers". Instead of using established elements, new elements which are not portable are created and used. Even worse, many websites still use Flash, JavaFX and Unity. With that, they could as well write their own plugins, doing exactly what they want. Or write a proper client instead of a website.
However, this looks to me like a sculptor forming his stones of concrete before working with it. Except for some special cases
when anything else is in fact impossible, thats nothing I really consider art.