Looking at the very bottom of that page, I do not understand how that function would prevent ASIC mining from being significant. You still need to compute a huge number of (SHA-3) hashes, and speeding these up could still make a significant difference, couldn't it?

I guess that in the limit, the speed-up is less relative to Bitcoin-style mining. Still, as long as modern CPUs are not memory-bound during computation of such hashes, ASIC miners would still win.

They will have the more interesting technical challenge of combining integrated hashing circuits with custom memory interfaces, though ;-)