In short, to achieve behavior similar to what you're describing would require ajax of some sort. The connection between the model referenced in the controller action methods and the UI is broken with every request/response cycle, so realtime updates of the model properties don't happen as you're used to in WPF.
The cleanest way to do this would be to create a SPA using something along the lines of AngularJS and use MVC's WebAPI feature to expose an API consumed by the client. This won't get you realtime property updates out of the box, but a good framework will help you organize your client code and avoid page refreshes if that is your design goal.