Hi both/all,
OSM contributor at the amateur level (2.5K edits).
I've watched and read about this construction project over the last few years. An empty dam that only fills when there's a flood risk downstream, in Skipton. The nearby Eller Beck Slow Release Dam (just NW) works in the same way and floods part of the golf course when it fills in flood conditions.
1- I've removed the amenity tag due to no match and left it as a dam.
2- There is the waterway:check_dam option on OSM ; although the function is similar this is a bigger structure than the examples given (https://wiki.openstreetmap.org/wiki/Proposal:Check_dam).
3- Wiki also records the flood defence proposal (https://wiki.openstreetmap.org/wiki/Proposal:Flood_assets); this does have a "dam" option but is currently only "underway". I've added a "Fix Me" suggesting changing to flood_asset:dam (if/)when the tag is available and a note that this is flood defence. 
I've "resolved" the note but more than happy for it to be unresolved if you don't agree with my solution.
:)