At the moment, videos are not playable in the Gallery (only a thumbnail of the video is shown). The opposite should be the case. :)
It's not difficult to enable video playback in Android, however: Android does not support the Theora video format natively, which a lot of our videos are encoded in. This will complicate things enormously.
This also encompasses T85766, since animated GIFs can also be considered "videos" of sorts.