For example, embedded FB post. In React you can deal with it using componentShouldUpdate and others. I don't know how to deal with it in virtual-dom (package), without going deep into patching algorithm.
Also, React goes with Flux, and Flux is a reactive architecture. So, if you treat React a separate module, the whole flux architecture is pretty reactive.
I think that author is completely right about the part, that React has the only one reactive part — its render function. But I don't see why it makes React bad. I think it is great, fast and easy to use.
By the way, virtual-dom is a little bit early to use for production application. For example, if you have some elements in your vdom, that are changing after you render it (i.e. like buttons, embeded posts, etc.), virtual-dom will be totally confused and unpredictable. For example, it can duplicate some elements on the page.
I believe it happens because vdom depends on its internal index to traverse real dom nodes. It is still a remarkably good piece of software.