Not to be grating but your problem sounds more like using the wrong tool for the job. DOM is not made to render video game UI, it is a bad tool to do so as you discovered yourself.
But putting even those games aside which use webview for UI, there are still video games made inside the browser, and for those, having sub-1ms rerender times with React is perfectly reasonable. We could get into immediate mode vs retained mode debates right about here, but that is a slightly different topic :D