Hello @bulldozer and welcome to AppImage. “No root required” means that you can run applications which do not need root rights without the need for installation.
With deb and rpm, the user needs to be root in order to be able to install anything. In contrast, AppImages do not need to be installed, and hence you need no root rights for installation.#
If an application needs root rights, this does not go away simply because the application is inside an AppImage.
I am not familiar with GNUnet or how it works. Can’t it run in the normal user account of the user running it, like most desktop applications do? An application (no matter whether running from an AppImage, a deb, rpm or otherwise) needs root rights if the application wants to edit system files in
If you want to run the application inside an AppImage as suid, you need to set the AppImage itself as suid. (Although extra care is needed if you run anything as suid - hence I would advise against it. Most normal desktop applications don’t need it; they can request additional permissions as required using polkit.)
Does GNUnet even offer an AppImage?