I've written an actual game, a 2D platformer.
If there's a domain where it's easy to demonstrate that the view is purely a function of the state it's precisely in gaming. In many games you can toggle (in dev or even for some during gameplay) between "the real view" and, say, wireframe view of the game (with lots of debug infos added too for example). Or you can toggle between a 3D view of your game or a top-down 2D one. Or you can toggle between different types of rendering (as in Diablo 2 where both a 2D and fake 3D view where available and the modern Diablo 2 ressurected, where you can you can show... The 25 year old view if you want to, at any time).
Many games are 100% deterministic and the entire game user(s) played can be recreated from only a record of the user(s) inputs (which is why some save files for long games can be tinier than tiny). And it'll replay the same on different screen configurations / different platforms.
The view in a game at time n is literally f(state n).