That's pretty good, but it's a categorical system and not a hierarchical system. Also "road bike" is not a term used on the site or in the standard since it encompasses many different types of bikes meant only to be ridden on paved surfaces. For the purposes of the standard, a paved surface and a road are not the same thing. So I don't think that's correct.
Also, upon further research it appears category 1 bikes do not often include any adult road racing bikes, touring bikes or other bikes meant mostly for paved roadways. Those are usually category 2, with gravel bikes being category 3 and mountain bikes being 4/5.