I now cleanly removed everything (with the exception of having used a registry cleaner) and reinstalled WACUP.
There is a special option to create a legacy file for making plugins work in other programs (AdiIRC in my case) under
Options > Preference > Advanced > Options Page 2 > Playlist Compatibility which I had checked before and which is checked now.
I installed WACUP under C:\Program Files (x86)\winamp\ and set both paths in AdiIRC accordingly:

The good news is: It's not saying
* /np: Your Media Player is not running, but the bad news is, it's only printing "
* @HtCwCjUeff is bouncing to ''" without naming the artist or title of the song.
Any ideas?