React doesn’t have to run client side. The DOM renderer is just one possible output, albeit the most popular. The output doesn’t even have to be human consumable.
That's like saying a ship doesn't have to sit in the water. You could put in in a dry dock too, and put wheels on it. But now it's not really a ship anymore. React, the UI framework, is a UI framework and is for user interfaces. The output _can_ be "not human consumable" but then it's not React, that's something else.