How to get correct grammar in the bibliography of a German document when the editor is an association?

If you are looking for a one-shot solution, you could add

 execute={\expandafter\def\csname abx@lstr@byeditor\endcsname{Herausgegeben vom}} 

to your bib-entry.

A more general solution would need some switches in the language strings (\ifwhatever{vom}{von}) and some bib field to set this switches -- possible but unclear if it is really worth the time ...-

This is one of the limitations of biblatex's localisation system.

As a dirty fix you can include 'dem' into the editor field

editor = {{dem Fachverband Latexology} and Doe, John},

This will give good output only if the editor is used in the 'herausgegeben von ' position. If it is used as in ' (Hg.)' this will not work correctly.

Since the citations give the short form you can use

editor = {{\ifbibliography{dem }{}Fachverband Latexology} and Doe, John},

to fix that.