A non human character I completely felt drawn into was the Alien of the original "Alien vs Predator" by Sega.
Few design decisions like a wide angle view, great speed of movement, the ability to climb on everything and a small infrared halo when seeing humans were very effective.
The identification with this creature "unclouded by conscience, remorse or delusions of morality" was so strong that for a while I found myself spontaneously spotting the dark corners and the paths to reach them in every room I entered in the real life.
And again the goals I was asked to achieve brought the story forward, but broke the magic, remembering me that I was in a video game and not just "there".