Safari creates Zero bytes instead of actually downloading files
Got the same problem again, googled my own question. 

As it turns out, where exactly you right-click makes a difference. I happened to be doing it on a progress bar, and that gave me the "Save Page As" option, which results in zero-bytes downloads. However, if you right-click the timer or the controls, it gives you a whole other dropdown with some media-related options, one of them being Download Video As, which works properly.

So the answer is:


Cmd+S won't work;
pay attention where you click and make sure you save via the media content-related dropdown.