Well, cryptographers have been contemplating a post-quantum world for some time now.
Quantum computing, although in its infancy as far as real-life computers go, has been studied in a theoretical sense for a quite a while. Shor's algorithm was published 19 years ago; Grover's, 17 years ago. These are the two most-famous quantum algorithms, I think, but the field goes back further than that: according to Wikipedia, the field was born somewhere in the 1980s.
The point is that even though quantum computing hasn't produced a usable, useful real-life quantum computer yet, it has been considered for quite a long while now. So while huge breakthroughs are still very possible, it's likely that researchers have exhausted all of the easy lines of attack. Further, since it doesn't seem that in the last 16 years any new, cryptography-threatening quantum attacks have surfaced (at least, none that I am aware of), it seems relatively safe to talk about post-quantum strength.
More to the point, the real threat against hash functions in a post-quantum world would be Grover's algorithm. Using Grover's algorithm, mounting a brute-force preimage search on an $n$-bit random oracle has time $O\left(2^{n/2}\right)$.
Although direct application of asymptotic bounds is rather imprecise, this would lead to a preimage attack in time $2^{128}$ for a 256-bit (preimage-resistant) hash function. This is still secure, and I think this is what the authors were intending when they said "post-quantum sufficient." For more information, see the question What security does Keccak offer against quantum attacks, specifically Grover's algorithm?.
