Your Airport Extreme has a link-local address.

Wikipedia:

For Internet Protocol (IP) networks, they are assigned most often using stateless address autoconfiguration. In IPv4 they are normally only used to assign IP addresses to network interfaces when no external, stateful mechanism of address configuration exists, such as the Dynamic Host Configuration Protocol (DHCP), or when another primary configuration method has failed.
Link-local addresses for IPv4 are defined in the address block 169.254.0.0/16

Just enter the setup and manually configure an IP-address for the ethernet interface of the Airport Extreme in the same private address range as the ethernet interface in the Cisco router.

Your Airport Extreme has a link-local address.

Wikipedia:

For Internet Protocol (IP) networks, they are assigned most often using stateless address autoconfiguration. In IPv4 they are normally only used to assign IP addresses to network interfaces when no external, stateful mechanism of address configuration exists, such as the Dynamic Host Configuration Protocol (DHCP), or when another primary configuration method has failed.
Link-local addresses for IPv4 are defined in the address block 169.254.0.0/16

Just enter the setup and manually configure an IP-address for the ethernet interface of the Airport Extreme in the same private address range as the ethernet interface in the Cisco router.

Example:
If the IP-address of the ethernet interface (Cisco Router) is 192.168.0.1 netmask 255.255.255.0 assign 192.168.0.2 netmask 255.255.255.0 to the ethernet interface (Airport Extreme)