I think the official app does let you download but its literally a file on your phone. So you need a file manager and a video player that can play your file in addition. There is generally no management of downloads or a way to see what you downloaded in the official app.

Findroid improves on this massively, I however keep having the issue it doesn't seem to download images from the library, so all my downloads are grey boxes. Just a cosmetic issue though as they all play fine.