> What if Apple pushed IIGS over the Mac?
The II was a dead end. The 65816 was not a nice ISA to program for. Very powerful for the clock, but going with the 68000 allowed the Mac to continue relevant up until the transition to PowerPC.
> What if Commadore had got behind the Amiga properly?
I think the best missed opportunity of the Amiga was when Commodore refused to allow Sun to sell the 3000 as a low-end Unix workstation. At the time, it was unclear whether Unix and its descendants would be the winner of the OS wars, but it would have been wonderful if the Amiga was launched with the same OS Commodore ported to their never launched Commodore 900 workstation.
> it would be possible to run Doom in a meaningful way on the original 1987 Acorn Archimedes
I bet there is a port for it. The first benchmarks indicated the plain Archimedes had higher FP throughput than a 16MHz 386 with a 387.
> Would a game like that have tipped the market in its favour if it had been there at launch?
I don't think I ever saw an Archimedes being sold outside the UK. I only heard of them because BYTE magazine had excellent coverage of interesting machines available abroad. I wish they would be more available in the Americas (back then I lived in Brazil)