In my understanding template would be the entire page. So while an an individual div re-rendering is also technically a template, it's not really the same thing. It's a tiny re-render compared to a page refresh.
Again, this is a different spin on doing things. Rails preaches abandoning the over-complexity of the client-side in the browser and pushing work to the server.
I personally love it. I'm sure someone who is as fast in React as I am in Rails is laughing reading this.