Log Files: ~/.config/unity3d/SphereII Software/ModLauncher/Player.log
Install Folder: ~/.config/unity3d/SphereII Software/7D2DModLauncher/
Regardless of where you run the 7D2DModlauncher, it will install in the above folder. Take a look in there and see if there's anything there.
In .../7D2DModLauncher/Player.log I find the only thing that looks bug-like:
..snip..
requesting resize 768 x 432
resizing window to 768 x 432
Desktop is 1920 x 1080 @ 60 Hz
UnloadTime: 1.789935 ms
Initialize Lock
NotSupportedException: Specified method is not supported.
at System.Threading.Mutex..ctor (System.Boolean initiallyOwned, System.String name, System.Boolean& createdNew) [0x00006] in <2b3a3162be434770b7a4fac8b896e90c>:0
at (wrapper remoting-invoke-with-check) System.Threading.Mutex..ctor(bool,string,bool&)
at SIDGIN.Patcher.Standalone.SingleInstanceControl.CheckInstance () [0x00000] in <879c2b2703464b50942117fbf745d5e7>:0
at SIDGIN.Patcher.Unity.SGPatcher. () [0x0001b] in <f4dd252254134fe8b115aa481e02276c>:0
..
Maybe?
I don't see any permission errors. There is another Player.log in ../7D2DModLauncher/ModLauncher/Player.log which has no error messages that I can see.
Let me know if you want logs and whatever else. Happy to try assist!