Google Chrome is now shipping with a download button for videos that are just embedded videos (i.e. not MSE):
The above answer offers a good solution. However, when I was working on this in my project, there were two problems with it.
Download occurs (as if the download button had been pressed) when right margin area of the fullscreen button is touched on Android (mobile or tablet). Applying z-index didn't fix it.
Because of overflow:hidden, the download button is invisible but still exists to the right of the fullscreen button. That means when you press "tab" several times after clicking any control button or bar on PC, you can still reach the download button.
Additionally, be careful -- some small-width devices (e.g. mobile phones) are small enough to hide the seek bar. It would need many more pixels to hide the download button.
I hope Google provides the option to adjust this ASAP.