I actually think this is "expected behavior", which is to say, its probably not possible at this time. Might think of requesting an enhancement through the https://community.esri.com/community/arcgis-ideas?sr=search&searchId=bda5ca95-b923-4b5e-8104-6e4d1d0... site - there might already be one submitted for this, in which case vote it up so Esri can see that we need more support for working with Related Tables in across their web platform!
I agree the functionality should be there, it probably should not be expected behavior since the controls are present to the end user.
Aside from submitting a bug to Esri and/or requesting this functionality in ArcGIS Ideas, a possible work around for the OP would be to use WAB's Filter and/or Query Widgets with the non-spatial table data. Results generated using these widgets can be exported to CSV, and the output CSV will honor the parameters that were set in the query.