More things that did not work, but should have:
Using Google Drive in Safari. Download never completes.
Using Google Drive in VLC (a poppular video viewing app). Download seems to complete, but never shows in the library.
I'm beginning to think there are some real problems with both the Google Drive app and the extentions on iOS.
Something that works, but shouldn't be this complicated:
I did manage to download a video from Google Drive using the GoodReader app. This is a good app for doing miscelanious things with files when no other app will do the job. You can watch videos in it, but it is not optimized for video. Instead, it's a PDF annotation app with the ability to download/manage almost any file type, and view most standard formats.
I then used GoodReader's tools to open a copy of the file in VLC. This should work with almost any third party video viewing app, as long as that app is compatilbe with the file's format.
This results in a copy of the app in both GoodReader and VLC. If you don't want two copies on the iPad (which you probably don't) you need to then delete the copy in GoodReader.
There are bound to be other apps that work directly, but these are the only ones I have to play with at this time. If you decide to do this and can't figure out how (GoodReader is complex), then let me know and I'll do step by step instructions.
VLC is free (with optional in-app purchases)
GoodReader is not, but might be worth your money for the other things it does.