A gateway is the same thing as a modem/router, so your AT&T device is acting as the main router for your network.
The DHCP and NAT setting on the AirPort would not be correct, since that will set up a situation where you have two routers on the same network both trying to control the network. So, the solution is disable the routing functions of the AirPort by changing the Router Mode setting from DHCP and NAT to Bridge Mode, which Apple calls "Off" (Bridge Mode).
The AirPort can still provide a WiFi signal if you want to use that for wireless connections.
If you leave the AirPort in the DHCP and NAT setting, that will result in an error known as Double NAT (or two routers). While this might work on a simple home network, it makes things more inefficient and will likely slow down your Internet connection as well.
This is why the AirPort Utility is recommending Bridge Mode for your AirPort. If you don't want to accept Apple's recommendation....(and mine)......there is a way to tell the AirPort to "ignore" the Double NAT error and the AirPort indicator light will turn green, instead of that annoying blinking amber. But, ignoring the error won't make it go away.
To change to the recommended Bridge Mode setting on the iPhone......
Tap to open AirPort Utility
Tap on the AirPort
Tap Edit in the upper right hand corner
Tap Advanced
Tap DHCP and NAT
Tap DHCP and NAT again
Tap Off (Bridge Mode)
Tap Done multiple times until the AirPort updates with the new setting
If you really do have firmware 7.8.1.......you have an AirPort Express.......not an AirPort Extreme
If you have an AirPort Extreme......there is no 7.8.1 firmware for that product. There is 7.9.1. though.