Hmmm, that's interesting, especially the System Report > Hardware > PCI which shows your graphics card. My Report does not show my graphics in the PCI area, only in the Hardward > Graphics/Displays.
Are you running the latest BIOS? What version of macOS?
I'm puzzled. I only thing I can think to do is to move it to another PCIe slot. Try several PCIe slots.
I am also running a GTX960 (4G Gigabyte branded wind force) which also is listed under PCI, but again under displays along with my monitor. Firewire picks up the card correctly though.
I just stuck all the parts together in my case, flashed and configured the BIOS as advised on page 1 of the guide and chucked in my system hard drive from my previous P55 i7 860 hack. Booted off a USB stick I made up before swapping all the components over and once I was working copied that over to my EFI. It all just worked for me and I have had no crashes or stability issues since putting it together. No reinstall or anything. I had to reauthorise some software licences but that was it.
At the moment I am running with no overclock or anything but doubt that would affect the firewire card being picked up. I had my previous machine clocked up considerably and had no issues with firewire on that.