Let's start with what equipment is available, and how you are planning to go about this.
1. Ideally, you should have a dual homed device (something with two ethernet ports) acting as a router between the two home networks. This will allow each network to be mostly untouched, and internet access to continue unimpeded, if that cable/device is unavailable. The alternative of using only a single DHCP server for both networks would be problematic if the connection between them were to be broken for any reason. An example might be a cheap GL.Inet router running OpenWRT, configured with static addresses on each of the home networks, and configured to route packets between the two networks (but not to the Internet).
2. Each home network would need to use different subnets. e.g. 192.168.0.0 and 192.168.1.0.
3. To instruct the gaming machines that need to speak to each other directly how to do so, you would need to add a static route to the other home network on each machine. i.e. on gaming machine 192.168.0.101, the equivalent of "route add -net 192.168.1.0/24 gw 192.168.0.2" (where 192.168.0.2 is the address of the router), and similarly on any gaming machines on the other network. If you are wanting to game on things like Xbox or Playstations, you may need to see if your home router can be configured to include the route in the DHCP response (but I don't know if xbox and PS can even do direct gaming).
If you want to do it without the intermediate dual-homed router, it is possible (in particular, disable one of the DHCP servers, or else capture the MAC addresses of the devices that should get addresses from the various DHCP servers), but you will effectively be joining the two networks together, and will most likely have all traffic routed by only one of the upstream connections.