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After researching this, it comes down to this:

When Droid Explorer launches, it attempts to start ADB in root mode by running adb root. If adb cannot run as root, you will have limited access to some paths.

Now, I run CyanogenMod 12 (this should also work with CM11), but I don't know if this can be accomplished with stock rooted ROMs.

These settings are for CyanogenMod
In order to allow ADB root access, I go in to Settings => Developer Options. There you will see Root Access:
Root Access

This needs to be set to either ADB only or Apps and ADB.

Adb only / Apps and ADB

If this is not set, Droid Explorer will not be able to launch as root. When it tries to get the folders and files of certain directories, it will be denied.

If you can, try running adb root from a Windows Console window and see what it returns. It may add some insight to if it is possible to have non-CyanogenMod devices run adb as root.