But I haven't written that input-process-output equals functional. I just pointed out that the React model allows for a larger piece of the code to be functional, in exactly the same way it's done, say, in Haskell. This has nothing to do with monads. Monads are used for the imperative, stateful code that is pushed to the top of the call stack, the bit which is partially managed by React for you (by calling the render method).

I would also never claim that React invented any of this. It just popularized this more declarative approach for building Web UIs