The "special" directories typically use the same nomenclature in the big DEs (Gnome, Unity, XFCE, and I think KDE), but the reason that's the case is that there is a more or less standard way of registering the "special" directories in the user configuration files using the xdg spec:
See
https://wiki.archlinux.org/index.php/Xdg_user_directories and
https://freedesktop.org/wiki/Software/xdg-user-dirs/Gnome, Cinnamon, XFCE, and KDE (to my knowledge) just query the xdg config files and use what's there for system operations. I know this for a fact with Gnome and XFCE, because I had to recreate the directories on a few systems after an accident. Just creating a directory with the proper name won't get a DE to treat the directories as "special" (i.e. save appropriate files there by default, index them, etc.), they need to be specified in the xdg config file in order to receive special treatment.
So it seems like having JRiver read the xdg config files (where available) and using those directories would be the standards-compliant way to do it, and would catch the majority of desktop environments. It would also handle corner cases where the directory names differ from the defaults for whatever reason (distro customization or user manual config changes). Xdg even supplies a utility to handle the queries (detailed in the arch wiki link above). Xdg is also how most DEs auto-handle localization for those directories, so it would be a potential labor saver for JRiver as well (no need to translate the directory names, etc.).