You should not have to download that data. It is already part of CesiumJS itself, in the packages/engine/Source/Assets/Textures/NaturalEarthII directory. When you build and start CesiumJS, you should be able to use this data as it is described in the linked documentation. If this does not work for you, then (I might try it out locally but) it could be helpful if you described the problems that you are encountering.