The Amiga, - like the Atari ST failed to crack the mass business market in the mid eighties which was the intention of both companies to achieve as IBM and Micro$oft had already sown up the market.
With this sad failure, both machines were left to re-invent themselves with niche markets (music and video production) and games only.
As such, the ST bit the dust first as the Amiga's hardware was superior and so was the better gaming machine.
If the Amiga hadn't been forced to become a major gaming machine (when it could do so much more) it would have died along with C= in the late eighties as anyone familiar with the companies profit margins at the time will testify.
So i repeat: gaming kept the Amiga alive in the short term, but the price was the misconception of it as a mere console with a keyboard.