Anycast is good in the absence of better options, but I don't think this is Anycast.
It sounds like here Amazon is doing unicast DNS, but dynamically changing the response depending on the IP address the query comes from.
Since they have a big database of IP addresses and latency, they can choose the best response.
The missing thing here is that they don't get the IP address of the client computer, only the DNS server. In many cases that (along with geo-location of the DNS Server) might be enough, but it is possible to do better. I'd speculate what they do here is correlate the IP addresses with the DNS server either by subnet or by using active measurement techniques.
It sounds like here Amazon is doing unicast DNS, but dynamically changing the response depending on the IP address the query comes from.
Since they have a big database of IP addresses and latency, they can choose the best response.
The missing thing here is that they don't get the IP address of the client computer, only the DNS server. In many cases that (along with geo-location of the DNS Server) might be enough, but it is possible to do better. I'd speculate what they do here is correlate the IP addresses with the DNS server either by subnet or by using active measurement techniques.