downloading stored YouTube file

Black Hole

May contain traces of nut
It is possible, because the web browser will probably try to play the mp4 rather than save it. I don't know why "nothing happens" though, I would expect you to see some evidence of an attempt to play (unless perhaps your security is blocking it).

This is a situation where wget might be better (a downloadable Windows command line utility, use the DLNA URL as the parameter), or FTP, or even Samba.