Delete and re-create the relationship classes in the GIS.WN feature dataset to set the privileges. This is how the related case was resolved.
Or
Use the Change Privileges geoprocessing tool to correctly assign privileges to the WN feature dataset.
Or
Case# 01747095, After moving the relationship class outside of the feature dataset the privileges window displays as expected.
NOTE: Tested this with the GIS.WN feature dataset and the privileges window displays as expected.