Trying to figure this out also - BUT with HDMI to Firewire...looks like I may need an additional adapter of male Firewire IEEE connection to female HDMI
I do have a FireWire 800 hook up on the back of my 2010 iMac to to my DVR (Firewire IEEE 1394 input) using a cable like this https://www.amazon.com/Clear-IEEE-1394-Firewire-Cable/dp/B00699GJW4 - The one I picked up was a Belkin about 6 years ago. From there I use a program called AVS Browser which automatically reads my DVR. Then I stream through VLC player.
Kind of ticked me off..just a little when I asked an associate at a local computer store this past week of FireWire to HDMI for video, in this smug tone he said - "huh? No such thing, Firewire doesn't work for video, just data" Yeah, 50% true! I wasn't even going to get into it, but yes Firewire WILL work with video connected to a DVR, The video stream is well "data" (NOT all channels on my Fios box works..some network are blocked and will not record. Many do.)