When the DHCP server is turned off, the Windows machines won't be given an IP address so they automatically give themselves one in the 169.254.X.X network. All the machines on the same LAN will see each other but they will have no gateway entry for connecting to other networks, even if your router did handle that network, so they won't be able to connect to the internet.
Don't know about AOE but maybe because the machines can't see the internet allows you to play a LAN game.