I guess what I don't quite understand in your comment is why these two categories of "web app" and "document" are so fundamental, in the sense that we can divide all web content into either document or web app. Is this a useful categorisation, or is it just applying concepts from existing forms of media to a medium where those concepts don't really fit that well?
For example, with the watch page, if we're defining document by printability, it makes a poor document - while you can print it out, what you'll end up with is a document with lots of static pictures and a bunch of (now useless) text referencing how you can move the pictures to see different things. If I wanted a fully printable document, I'd find a different one that was written with the expectation of being printed - maybe a book about watches, or an entirely static page. That will suit the print medium significantly better than this interactive page.
It makes me think a bit of a science museum, in the sense that most science museums will have a lot of text written around that explains all the concepts they want to discuss - this is how a pivot works, that's what a cow's digestive system looks like, here's a description of a space ship or whatever. And you could collect all this text and turn it into a book, and it would be an informative book that you could read and thereby learn something.
But the value of a museum is that it doesn't just have to be text. You can put a pivot into your visitors' hands; you can show food moving between different parts of a cow's digestive system in real time; you can show genuine pieces of real rockets and discuss what journeys they've been on. The medium allows you a huge amount of extra freedom, and a good museum curator will use that freedom - wisely - to produce an experience that allows visitors to get more insight than they would have if they'd just "printed out" the museum's text and read it all.
That's not to say that written text doesn't have its own advantages - you don't need to visit a book every time you want to get information from it, for example! What's key is that by tailoring the content to the medium that we're employing, we can produce a better result than by trying to apply the norms of a different medium. If we'd built our museum like a book, it would have been a bad museum.
I think a similar principle applies to the web - it comes with its own set of tools and features that differentiate it from books or print media. Some of those are fairly subtle - the ability to reference different pages and sites using hyperlinks, for example - but part of that is the interactivity. And not all sites need interactivity at all times, and the best sites use interactivity only when it adds to the experience (just like the best museums - not the ones that surround you with flashing lights and noise just to distract your attention). But the use of interactivity can elevate a simple text far beyond what a print document can do. I think the watch site is a really good example of what happens when you don't see web pages as "just" documents, and rather embrace their unique qualities.
That's why I don't think it's always helpful to make this category distinction between "document" and "web app", particularly when "document" just means "uses the norms of a different form of media", because the whole point of the web is that it a new media form, with its own features and capabilities.