Took a while to investigate.
The xdg-open app is a shell script, part of xdg-utils. On
Slackware
the file is installed to /usr/bin.
The script offers no support for Trinity. Perusing the script
indicates a poorly written script rather than anything robust. No
error-checking or "idiot-proofing" at all. The script provides no
optional methods of detecting the desktop. The presumed desktops
are hard-coded and the "generic" functions are poorly written.
On my system anything I try to open wih xdg-open is opened in my
default browser, Firefox.
I tested in KDE4 and everything works but only because KDE is one
of the few supported desktops.
I have no idea why GIMP is opened. The user could edit xdg-open
and
add some echo statements to help debug.
Setting DE=kde doesn't work in my GIT setup. The reason is in GIT
we changed the environment variables, but 3.5.13.x still uses KDE
environment variables. Hence the partial success.
Other than submitting a patch for xdg-open to upstream I doubt
there is little we can do.
By the way, xdg-mime is another script from xdg-utils and the
similar presumptions are in that script. The only supported
desktops are KDE, GNOME, Xfce, and LXDE. Otherwise the desktop is
presumed to be "generic."
The Arch folks have a discussion about xdg-utils and they say xdg-
open is broken.
https://wiki.archlinux.org/index.php/Default_Applications
Searching the web for "xdg-open" indicates the script has been
broken through the years. As I wrote, the scripts are not robust
and contain limited presumptions. :-)
Darrell