Your code works very well right now with one store and one view controller. When you start needing multiple stores and multiple view controllers, you'll find that you're writing the same code over and over again.
Pull out the parts of AppContainer that are specifically about binding to a store, and put them in a React component of their own. Use the higher-order component pattern and not the mixin pattern. In the end you should have a reusable component that any view controller could use to bind to a store.