Chrome 55 introduced new media (video, audio) controls that included, by default, a download icon. There were, as expected, howls of protest, since there was no easy way to turn it off. Site visitors were always able to download the video (right-click, "Save video as..."), but having an icon there made it very obvious.
This will be fixed in Chrome 58. Here's the writeup:
https://developers.google.com/web/updates/2017/03/chrome-58-media-updates#controlslist
Happily, other browsers will simply ignore the new
controlsList attribute, so it's an easy matter to include it in your code if you're using the native HTML5 <video> and <audio> tags.
Edit: Note that this will only remove the download icon. It will still be possible for site visitors to download the video by right-clicking and choosing "Save video as..."