So it looks like your GPU supports h264, hevc, vp8 and vp9 acceleration.
You could also try creating a file containing this: Section "Device"
Identifier "Intel Graphics"
Driver "intel"
Option "DRI" "crocus"
EndSection ..naming it 20-intel.conf, copying it to /usr/local/share/X11/xorg.conf.d, exiting to the console prompt and "startx" again - this might get rid of the 965_dri.so error you saw in /var/log/Xorg.0.log.
You can now look under "about:support" in firefox and scroll down to "Codec Support Information" to check if hardware decoding is supported.