I'm late but "late" is better than "never":

*Can anyone explain what dnsmasq is doing here?*

 - query[A] = resolution request for IPv4
 - From: obviously the source, as you already stated, your router's public address.
 - forwarded to: is the URL forwarding to the DNS servers that you configured for such kind of URLs, in case that no config there, is using the default DNS servers or your GW.
 - reply: the DNS Server is not being able to resolve the host because that domain doesn't exist (mymovies.home) and therefore is delivering that "NXDOMAIN" as reply
 - 192.168.1.124 is the IP that you have statically configured for mymovies

So was, hope that somebody still finds this useful.