Yeah, no router involved here... just a switch.
Without a router, there's probably no DHCP server. That's quite fine, as you seem content with assigning the network info manually.
The
gateway address refers to a router, so no gateway needs to be specified unless you need these computers to access the Internet, in which case traffic has to be routed from one network to another.
The DNS address does not need to be specified either, unless you need Internet connectivity or have to resolve host names. If you plan on using a gateway (router), your DNS would probably be your gateway IP. If it is necessary, Windows hostnames can also be resolved using other methods... Again, not necessary for your situation.
If you
have to specify a gateway and DNS, then you should enter the IP address of the game host computer for the values. I say
'have to' because I've noticed at least one game over the years where clients could not detect hosts until the gateway and/or DNS was supplied... Even though it isn't really necessary.
But in short, just an IP and subnet should get your by. Gateway and DNS would only be useful for Internet connetivity. And a router really would be an easier way to do all of this... Just a cheap one... Plugged into one of the ports.