The layered parallax scroll was the reason I linked to that time position. 
Of course, it's possible to do any game with any machine, if you're willing to remove features. Fewer colors, blockier scrolling, flickering sprites, slower update speed, simpler sounds, etc.
I wonder why other manufacturers didn't learn from Amiga's Copper chip. Being able to write the display control logic in copperlists was a huge enabler in making all the arcade-like graphics possible. Just think what a difference it would make if you could change all parameters and addresses on the fly, with simple control code programs that the video chip runs autonomously in perfect display synchronization without any CPU intervention, no interrupts or anything. If you could trigger any VDP parameter change at programmable screen row/column addresses, trigger blitter commands...
In a sense, the Copper is what makes Amiga's graphics hardware resemble modern GPU shader programming, even more than the blitter. The Copper turns the whole thinking upside-down. Instead of writing CPU commands like "do this manipulation work, and when it's ready, re-check everything, where we are again..." you can write a command for every screen position. It's not possible for a Copper command to "take too long". In some way, writing a copperlist feels like writing a pixel/fragment shader.
