The A380 was proposed well after etops-120 was widely utilized by airlines, and etops-180 was announced in 1988 with airlines taking advantage of it relatively quickly. These were certainly were not new unexpected market conditions the aircraft faced after production.
So, you're right, APU cannot deliver trust, but...
I just looked into it, I cannot find a definitive answer (without spending hours reading actual legislation, and I don't want to), I think the situation is that some manufacturer use the APU to provide all electrical power in case of single engine operation as a way to leave 100% of power for trust to the one engine that works in order to meet the ETOPS time/distance requirement. In those cases, there are extra regulations around the APU needing to be able to be started at all altitudes etc...
In order words, and again if I got that right, you don't need a special APU to be ETOPS, but you can, and if you do there are more constraints on the APU.
I believe all ETOPS planes need to be able to start the APU at maximum certified altitude.
Interestingly, until recently the 737 (which was not designed with ETOPS in mind) had to leave the APU running for the whole duration of ETOPS flights. It took a few years of data gathering before the FAA was sufficiently convinced that a cold-soaked 737 APU would start at cruise altitude. They now are, and "APU On-Demand" is now used on 737 ETOPS flights (i.e. Alaska Airlines flying west coast US to Hawaii)