Yes I know how it won't show up without a river  But if you look in the technology tree, it isn't even present for the Empire races.  Try this:

1.  Create a new game with any Kingdom race, look at tech tree - Civics, and you will see the Water Wheel shows up there,

2.  Repeat with an Empire race and you'll see that it does not.  And it really doesn't, if you have a town by a river etc the option to build a Water Wheel never comes up for the Empire.

- Manii Names

This is WaD (working as designed).  The empire doesn't get Watermills, only kingdoms do.  Conversely Empire players get Skath Pits.  Skath Pits aren't quite as good (and they don't come as early), but they don't have the river requirement.  Empire players are better at surviving in less ideal locations, Kingdom players can generally make better cities.

You are right that we should do a better job of displaying that these improvements are Kingdom or Empire only in the Hiergamenon.

Much appreciated.