Neat video, but it misses other aspects that made the Amiga clearly superior: The sound and the animation capabilities. The title screens are a very tiny aspect of the game. The Amiga also had a much more sophisticated and superior operating system.
We need to bear in mind that, when the Atari 520ST first came out, Commodore only had the Amiga 1000. An Amiga 1000 system would cost almost three times what a similar Atari ST system would cost in 1985! It wasn't until two years later did we see a price-competitive Amiga 500, and it still cost more than a comparable ST system (though not by a whole lot; maybe $100 or so).
The Amiga and the Atari ST came out at almost the same time; the ST may have beat the Amiga by a month or two. Don't forget that the Amiga used to be the Lorraine owned by Hi-Torro, and was almost bought by Atari! I wonder how much of the Amiga's design concepts Atari "Stole" to complete their ST?