In the example above it looks like they are telling the server to listen on 192.168.12.2 and 192.168.13.2 specifically and to only answer requests from that address.
Correct, but they are saying “it would be nice if mt-daapd did this”, which in fact it does not right now.
Is this possible? Basically I want my server to be available on one network and not another.
Not exactly like that, no.
But if you use howl or a third-party mdns server, you could tell *that* to only advertise on a specific interface, and firewall port 3689 on the interface you dont’ want it to work for.
Or, firewall outbound traffic to 184.108.40.206 on the interface you don’t want people to access it on, as well as incoming traffic on 3689. that would work too, by supressing the advertisements and blocking access to the daemon.