For views, you either get some form of MVP, with explicitly implemented model interfaces that provide the glue between the views and the object tree they are representing, or data binding that effectively creates that same glue for you. Here's an example from UWP:
So no, it's not really functional. Quite the opposite - the state is global and mutable, and UX actions that purport change things really change them. That also makes it all very intuitive, though.
The concept is somehow complex to master, I compare it to getting monads to click, but when you understand it, you are able to envision how to build the full UI architecture as having a Lego box at your disposal.
For everything, views, stylesheets, event handlers, data models.