React only needs a render method, not a render method and an update method for every state transition. Without the virtual dom this would destroy performance, so it is a rather key detail in understanding React's appeal.
FWIW we are trying to avoid "virtual DOM" in the new docs. The thing you create in render() and that describes the tree has been called "a React element" for many versions by now. "Virtual DOM" was more of a marketing term and I find it misleading because it doesn't make sense with e.g. React Native, and also makes React seem like a performance trick. React is not a performance trick. That elements get compared by React DOM renderer is its implementation detail. React is abstraction for dividing UI into predictable pieces, not a performance optimization.
If I wanted to do what React does, but without React, I might start like this:
document.innerHTML = myComponent.render();
That way, I can write components similar to React components and it can render very quickly. However, this strategy would work only on the initial render, because this naive strategy would destroy implicit DOM state like scroll positions, focus state, and cursor selections. The React DOM renderer (formerly known as the virtual DOM) lets me apply this rendering strategy without ruining implicit state.
The DOM renderer does not give me components or performance, since I can already achieve those things with raw Javascript. What it gives me is the ability to use a simple, clean rendering strategy without destroying the DOM state. That's why the React DOM renderer is not just an implementation detail.