I don't think using a mapping is the best idea for providing DNS to your client computers. There is a DNS Server in WinGate that will listen for DNS requests from your client computers and then ask an upstream DNS server for you already.
The DNS Server in WinGate is
very straight forward and should require little to no attention to make it work. It listens for connections on port 53 from the network adaptors that it is bound to, and then it will find a suitable DNS server to forward the requests to from the network adaptors settings on the WinGate computer.
If the computer is running an Active Directory, you will need to disable the DNS Server in WinGate and let the Microsoft DNS Server handle all Internet DNS Requests for the network.
Make sure that the DNS Server in WinGate has successfully bound to the network adaptor that your client computers are connecting to. `Gatekeeper -> System tab -> DNS Server -> Bindings`.
The DNS Server cannot require authentication from client computers for DNS requests, so make sure that the DNS Server allows unauthenticated access to the guest account in it's policies, and make sure the guest account is enabled in the User Database.
If the WinGate computer is a member of a domain and there are DNS settings that point to an internal ADDNS server, you can stop WinGate from sending DNS requests to the ADDNS servers IP using the Advanced Options. `Start -> Programs -> WinGate -> Advanced Options -> DNS Servers`
You can manually specify the DNS servers that WinGate should use in WinGate. If you are having problems making WinGate send DNS requests to the correct DNS server, you may need to use this option. `Gatekeeper -> System tab -> DNS/WINS Resolver`.