The general premise is that in practice templates usually end up very tightly bound to the view using the template, so you're not actually gaining anything by putting them in a different file and there's a lot of downsides to using a different language for templating.
Having watched the talk now, I see what he's getting at. I have maintained, at most, a small-approaching-medium-sized single-page app, and it was an internal tool. Clearly I have not felt any of the same pain that inspired React.
But within that particular experience, despite my "underpowered" templating tools, I've settled on a style that very close to what he calls "components", built instead from pairs of one partial and one viewmodel. Tightly coupled (cohesive?) within each pair, but as a unit are reusable together elsewhere in the front-end app.
So I can agree in theory, and see where my ideas have wandered close to the path that React takes. Really the only thing to do now is try it on a substantial project to see how it compares in experience. I suspect I'll still feel the urge to want the JSX in a separate file in some cases.