Taking that as a given, my question is, why does the author of this post, and the people he's talking about, miss that hypertext can already do this?
It might be that the issue is UI, both on the producer and consumer side.
Production of hypertext is difficult if it requires writing HTML; WYSIWYG or "personal wikis" or other hypertext-production UIs like that improve this. Maybe they're still too cumbersome, relative to Twitter? Hosting is also an issue - there are a lot more places you can sign up for an account and post things in a Blogger/Twitter/Facebook-style linear feed than host free-form hypertext.
I think a more interesting issue is the consumer side. We have good UIs for consuming linear streams of content as they get created, but it's not immediately obvious to me how you'd make a similarly good UI for consuming updates to a web of hypertext. Maybe you could consume diffs? The problem seems somewhat similar to serialization of an object graph.
Of course, the notion of "consuming updates" to hypertext might be entirely the wrong perspective - again maybe there are some insights from the analogy to an object graph.