I'm guessing that you previously had an extension installed that enabled you to download videos, and that after upgrading, the extension is gone.
You'll have to figure out which one it was, and re-download and re-install it.
But be careful!
I believe that before installing it, you -might- have to disable System Integrity Protection
To do that, you need to
1. Reboot to recovery partition
2. Open Terminal
3. Enter this command: "csrutil disable" (you'll need to write it down, no quotes, and that's a space character between the two words)
4. Reboot once again.
Once installed, you can re-enable SIP by repeating the above instructions, and this time use:
"csrutil enable"
Final thought:
I've pretty much given up on Safari for downloading video.
If I want to download (from YouTube, etc.), I use Opera or Firefox.
Apple seems to be trying to discourage such extensions with Safari lately.