Hey, Deathmask! The first released FPS on the Amiga - or so they claimed, if I remember correctly it did not have free movement, you had to turn in 90 degree steps and move a map square at a time, like eye of the beholder.
And then Gloom - I have to say I really liked this, it beat AB3D to the punch as well, although it was a good deal less subtle in gameplay terms, it was free-moving, and pretty action packed. Some nice touches too, like how you could find a Defender arcade machine and actually play it in-game! ;-)