ICMP destination unreachable to DNS server?

I totally agree with that explanation. The DNS client's timeout for arrival of a DNS response does exist, and in your case it is shorter than the server's response time. After expiration of that timeout the client unbinds from the socket, causing icmp destination unreachable to be sent in response to anything arriving to that socket, including a valid DNS response.

If you are interested in details, you can create a batch file like

@echo off
for /l %%x in (1, 1, 60) do (
   echo %%x
   netstat -p udp
   timeout 1
)

run it with output redirected to a file and initiate, from another window, the DNS query which you know will fail this way. In the output file, you should see for how long the DNS client keeps the socket open.