The problem is that applications want to put and look for stuff in ~/Library/Application Support/app-name folders so if you want to try the following as an experiment let us know how it goes:
cd "~/Library/Application Support/"
---make sure the OpenEmu application is not running before proceeding---
cp -pR OpenEmu "/Volumes/G-DRIVE mobile/Applications Support/OpenEmu"
mv OpenEmu xxx-OpenEmu
ln -s "/Volumes/G-DRIVE mobile/Applications Support/OpenEmu" OpenEmu
Note the consistent naming of "Application Support" as opposed to "Applications/Support Files" in your example to maintain consistent location strategy (not important but less confusing I think). I renamed OpenEmu to xxx-OpenEmu in case there is a problem so you can go back to the way it was if needed (just trash the new "/Volumes/G-DRIVE mobile/Applications Support/OpenEmu" folder if there was a problem as well as the soft link).
Another thing to think about is to simply relocate the entire /Users folder to another volume -- this would let you keep everything together as it was designed to be. Not sure if SIP would allow this or not. I used to do something like this on a Yosemite system, but that was before SIP. In any event you have to make sure the other volume is large enough to store the entire /Users folder before trying to copy it. And you would need to copy it in a special way that maintains permissions, attributes and ownership. And you would want to modify the /etc/fstab file to automatically mount the new volume in place of the /Users folder -- do a "man fstab" and "man vifs" to see how to do that (it has examples).
Is that what you had in mind? By the way is the "G-DRIVE" volume NTFS or HFS+ or ??? -- not sure if this will work if it's not HFS+
Good luck...