Update 10-28-2016: Update to the discussion of the request fields.
When using the Google Drive Java Client Library to list a user's photos and videos in your app, the thumbnailLink property is empty.
As far as I can tell, there is literally no good documentation on the solution for this. However, with the help of a co-worker and the REST API operations, I've gotten the solution.
To get valid thumbnailLink values, you have to make sure you specify the thumbnail field in your request. Since you're doing a custom field request you have to be sure to add the other fields you want as well:
Drive.Files.List request = googlDriveService.files()
.list()
.setFields("files/thumbnailLink, files/name, files/mimeType, files/id")
.setQ("Your file param and/or mime query");
FileList files = request.execute();
files.getFiles(); //Each File in the collection will have a valid thumbnailLink value
A sample query might be:
"mimeType = 'image/jpeg' or mimeType = 'video/mp4'"
Hope this helps!
Note that there is a difference between the Google Drive API for Android and the Google Drive Java Client Library. The latter library allows you to do more advanced things, like actually get all the files for a given account, not just those created by your app. The following link has a really good guide on getting started with it:
https://developers.google.com/drive/v3/web/quickstart/android
Oddly, I can't get the file query to work as it is on that quick start. But using my above query works great, so perhaps start with that.