It's astonishing to think that the Amiga hardware was done in 1984 and the A1000 came out in 1985 - the same year the NES released in the US! It took Nintendo until 1991 to come up with something roughly comparable power-wise.
From what I understand in the US the Amiga slowly petered out without never truly taking off. In Europe the A1000 never was a thing, but we had four years of the press talking about this mythical monster of a machine and its custom chipset. Then in 1989/90 all of a sudden everyone bought A500s to play Kick Off and Speedball II. That 89/92 period was glorious.
At least in southern Europe Wolfenstein wasn't regarded as a killer app at all, it barely made an impact. Doom and Wing Commander most definitely were, though.
The Amiga was less popular in the US and used more for graphics, sound and video for TV and movies on the 1000, 2000, 3000 and 4000, and with the Video Toaster, but you wouldn't see one as often when you visited people at home.