They should have bought a router, not a switch. A router gives out IP addresses, a switch doesn't. Don't worry though, because you can still make this work by assigning static IP addresses to each computer. Assuming you're using Windows XP, right click on "My Network Places" and select "Properties". Then right click on the icon that represents the ethernet card you have, and select "Properties". Then select "Internet Protocol (TCP/IP)" and select "Properties". Check, "Use the following IP address" and put:
IP address: 192.168.0.1
Subnet mask: 255.255.255.0
Default gateway: <leave blank in this situation>
Do the same for the other computer except enter the IP address as "192.168.0.2". This should work for gaming. If this doesn't work, make sure both computers are on the same workgroup.