As of collaboration ... it could be clients/single-server or fleet of apps synchronizing with each other. Gut feeling: later one has greater potential. Can work in standalone and team modes, no?
Imagine a developer and a designer working together on an app. The developer is writing the backend code for the app in the syntax he is comfortable with, and the designer is making the UI in something like Sketch. With Eve, this workflow will blend together seamlessly.
The counter() function you're referring to was implemented in GridEve, which was an experiment on the UI. It was written in C# and used a different (and abandoned) backend. It was a local-only app, so the timer ran on the local machine.
Time in the client/server architecture is something we have to give a little more thought to, since we're still trying to get things working in a timeless world.
But one of the nice things about Eve is that it effortlessly distributes to multiple nodes/users. So yes, we support the case where users are working cooperatively on the same document.
For example, that's the way the REPL works. Let's say my team is making a website about dinosaurs. On my machine, I add a stegosaurus entity to the database with several attributes: discovered, average length, average height, etc.
Now my colleagues have immediate access to this information. If one of them had a query open asking "What dinosaurs are in the system?" then their view would update with stegosaurus immediately.
In turn, I could use her list in another way e.g. to render it in a browser with links to each dinosaur's Wikipedia page.