In short, no, html is read-only. The clue is in the name: hyper text markup language.
The moment you have some kind of dynamic update, such as the comments boxes on that site, there needs to be something on the server side to receive the text and update a data store so that new views of the pages can show the changed information (the profile with the comments). Server side isn't html, it doesn't do what is needed.
Website can do lots of clever stuff on the client browser side to make it appear dynamic but the acid test is can someone on a different device see it - if they can, the data update has gone via the server. The clever stuff is usually a mix of html, css and javascript or something else entirely such as flash or an embedded java application.