I think this can be generalized as: if you need to break out of "click and wait a moment and see a changed screen" paradigm, for something like a continuously scrolling map or a smoothly flowing server load graph, then you can make good use of client-side loading.
Exactly. But why a blog platform or news site or other content-focused website would feel the need to do that is beyond me. Not everything on the internet needs to be an app.
If you are just trying to re-create it, don't.