I noticed this in the debug environment where I have to do many re-installs in order to test persistent data storage, initial settings, etc... It may not be relevant in production, but I mention this anyway just to inform other developers.
Any files created by an app in its App Folder are not 'visible' to queries after manual un-install / re-install (from IDE, for instance). The same applies to the 'Encoded DriveID' - it is no longer valid.
It is probably 'by design' but it effectively creates 'orphans' in the app folder until manually cleaned by 'drive.google.com > Manage Apps > [yourapp] > Options > Delete hidden app data'. It also creates problem if an app relies on finding of files by metadata, title, ... since these seem to be gone. As I said, not a production problem, but it can create some frustration during development.
Can any of friendly Googlers confirm this? Is there any other way to get to these files after re-install?
It looks like Google Play services has a problem. (https://stackoverflow.com/a/26541831/2228408) For testing, you can do it by clearing Google Play services data (Settings > Apps > Google Play services > Manage Space > Clear all data).
Or, at this time, you need to implement it by using Drive SDK v2.