Even after this explanation, I feel I'm just too dumb to understand the benefit. I'm not being negative, but until I see a real use case, I'm just don't see how this fits.
You're not alone. I don't understand the benefit either and the examples confuse me even more. The JSFiddle example[1] brings me back to the days of tightly coupled Views and Controllers which I've spent the last six years trying to keep loosely coupled. The interesting part is that tight View-Controller coupling is touted as a feature.
> By unifying your markup with it's corresponding view logic
So I've used Backbone and now I'm using Angular. I work a lot with D3, creating SVG's in "render"-type functions (still grokking how this all fits in with Angular directives, but that's another story). One benefit from this article that jumps out is the smart rendering that React does.
If you had a scatterplot with thousands of points, being able to add or subtract a couple without re-calculating the whole thing would certainly interest me.