Furthermore, the input-process-output model can hardly warrant being called "functional" in of itself, unless you really want to overload the term.
The React way of independent handlers that trigger events which incrementally calculate state and update views, is, in fact, quite similar to how Smalltalk UI paradigms work, right down to the installation of an event handler resembling a message send operation.
If you don't believe me, check out the Morphic framework that Self uses to implement its environment UI. The similarities are striking: http://handbook.selflanguage.org/current/morphic.html