This is rather vague.

Let's take a more concrete example:

Let's say you want to add a button somewhere that hides/shows another widget. Surely you don't want to go to the backend to do that? So how do you do it? With the store approach, clicking the button creates an action, that modifies the store (changing a visibility parameter somewhere) and repaints the UI.

In the diagram there is no flow back from the "API" box to the widgets. Though it still something that needs to happen.

The "API" necessarily contains some state, at least to track which component needs which data.