Probably the IP address belongs to the airport (from which your internet access is coming, since there's no cell signal at the plane's altitude) or to a nearby tower (which might as well be installed in the airport), and the internet connection is just relayed to the aircraft.
Doing some searching around, I found this: How does Wi-Fi work on airplanes?, which describes something similar:
Ground-Based Cellular Networks
In a ground-based system, an antenna located on the bottom of the plane transmits and receives signals to and from ground-based towers and works in a similar way to mobile phone networks. The plane's antenna transmits signals to the nearest tower, which in turn relays the signals to a ground station. The ground station retrieves the necessary data, which the cell tower broadcasts to the plane. As providers erect more towers, the area covered by the network expands. For faster expansion, existing cellphone towers can be fitted with the necessary equipment. Due to FCC regulations, the network is not available below 10,000 feet as the license is only for aeronautical use.
And from US Airways' description of the service:
Gogo has a network of cellular towers throughout the continental U.S. that allow transmission of broadband internet connectivity to Gogo-equipped aircraft. Three small antennas installed on the outside of the aircraft (two ATG antennas under the aircraft and one GPS antenna on top of the aircraft) receive the signal and send it to the Gogo system aboard the aircraft. The Gogo system then transmits a Wi-Fi signal inside the cabin for passenger use.
Also I would assume those services use some sort of cache, which might as well be installed at a server in Atlanta (home of Delta, as noted in a comment).