Activation of Delightful Downloads 1.3.6 generated "Das Plugin hat keinen validen Header." (The plugin does not have a valid header.)
Research pointed to a problem with my site's German umlaut characters (ä, ö, ü), even though charset utf8 was already in the wp-config.php file. Someone reported in another forum that the wordpress utf8 umlaut problem seems to recur with a lot of plugins.
My solution was to install and activate another plugin: Full UTF-8 (https://wordpress.org/plugins/full-utf-8/). I could then activate Delightful Downloads.
Seems to be working successfully now. Fully localized in German too, so hat tip to the translator.
This is merely a report for anyone else who may be suffering the same issue. Please mark this as resolved.