More specifically, he's manually adding and keeping track of all DOM elements. Once elements need to be updated, he would need to go back in the DOM and manually add/remove/change elements.. welcome back to the jquery messy world. Whereas with React, the render function doesn't change because it gets smartly rerendered.
Also, as far as I'm concerned, jsx is a big part of what I like about React. Basically, being able to add html from javascript instead of using all kind of hacks.