Regarding alternative formats like JSON or PDF, I guess you can add a layer there.
The way it is different is that it is an inversion of control inside the template, not that it is changing up the layering. You still have a "construct data" layer and a "present data" later, and you can still swap out the "present data" layer with something unrelated, such as a normal template engine or whatever else you wish to use to generate JSON or PDF.
However, inside the "template", rather than having HTML with embedded logic (where you can almost envision the HTML calling into the logic to insert text or execute flow control at specific points), you instead have logic that manipulates the HTML via DOM, modifying the HTML to contain text at specific points. You could probably even make a compelling argument that these are duals of each other.
What we've generally done as an industry is accept the former, but I'm not sure whether one is better than the other.