For the security, if all of your wireless devices are capable of WPA, that's more secure than any version of WEP.
Unless you set the new Airport up 100% the same as the old Linksys (same SSID, same security protcol, same keys, etc), your other devices won't be able to use the new network without some config changes being done to them.
Go thru the process of setting up that gaming adapter again and it should connect to your new Airport.