Is this the same process with the P4 remote control to enable the Fatshark Dominator HD2 goggles to work on HDMI

Yup, you buy the HDMI module from DJI, the module is the same for Phantom 3 adv/prof, Inspire 1 and Phantom 4. Remember to update your RC to the latest firmware after you installed the HDMI module (even you already had the latest firmware before the module installed).
I found that fat shark dominator 3 is perfect match for DJI Phantom 3 adv/prof, Inspire 1 and Phantom 4 because it display 16:9 video format.

Correct, it is the same for the P4.

Thanks guys