The individual site may be constructed individually (maybe) but it can only work if the society of people-who-use-the-internet all agree to follow a series of conventions about how websites work; you can't start using \<soul\> instead of \<body\> and expect everything to work as normal, because the reason the \<body\> tag is used to define the body of a page is because we needed a way to make sure people can use a webpage without having to define an entire new language for each one.
But no, a website is not a social construct because you don't have to have a society to have a website. I can have two machines connected and host an html file on one of them and stare at it on the other one all by myself and it will still be a website on a web! No contractual agreement is necessary!
But anyway, it's amazing that you posted on my comment! I am a huge fan!