I don't see anything that requires that the key be delivered over the net. I just did a test with Clear Key where the page with the video playback has a text field that the viewer pastes the key into, and that worked [1].
The scenarios I'm envisioning involve sharing videos between people that have good non-web methods of communicating, so can distribute a video's encryption key via some non-web means. End user encryption applications tend to by usability train wrecks for non-tech people (heck, they are often terrible for tech people, too...), so what I'm going for here is trying to get rid of the video viewer having to go outside their browser to deal with viewing an encrypted video.
Maybe this can be done with MSE without EME, by handling the decryption in JavaScript?
[1] Based on the Clear Key sample here: https://www.html5rocks.com/en/tutorials/eme/basics/
If you mean that the recipients of the video are restricted in what they can do with it, that's a DRM use case.