Your video files should go in a folder called "media" and not video, if you drag your video file onto the stage then this folder will automatically be created and the video file copied over.
I tried in both the ways you told me, naming the folder "media" and also dragging it in the stage but neither of them did work. it almost seems I can't import it because the format is not supported but it is an mp4!
I also tried with different videos and in different project files but it still doesn't work, anyhow the "video" tab in the library should always be there but it doesn't show up...
Are you using latest version? if the video tab is missing then i'd recommend reinstalling the software as some thing looks like it has gone a little screwy.