As it is right now, the FAQ's definition "behaves like an application" might not be helpful at all.
I instantly know the difference between an application (like Microsoft Word) and a document (such as a
.docx file created in Word) that's running on my OS, but that becomes very difficult on the web. I know that Remember the Milk is a webapp and that a 1990s "John Doe's Home Page" is not. But it's not always that easy to distinguish. Is a weather site a webapp? (You can interact with the weather maps, and I have apps on my computer that do the exact same thing.) How about a search engine? What about a choose-your-own-adventure story that uses HTML links?
Until there's a separate site that covers non-webapp sites, we're unlikely to have a clear line between the two. It's easier to define something by what it is than what it isn't. Without a separate site, it's a lot harder to stay on top of this definition because the choice is between leaving a question open and closing as off-topic. With a separate site, we can migrate it to another site; a user can follow the link to that stack exchange site and get plenty of examples that help them learn our definition of the difference between a web app and a website.