So, according to that map, since GMT is pretty much a strait line running from North to south pole, it would go strait down the center of the map. Therefore the International date line, on this map would run from the north pole, between Alaska and Asia (Bering strait), and loop around the side of the map and end up hitting Antarctica from the bottom side. The line is a bit jagged compared to GMT but it is the endpoints that matter here.
Using what we know of Timezones, this means when the sun is on the bottom side of Antarctica, on the international date line, we know that it is Noon all along that line, all the way up through the bering strait (sp?). It would be about 1-2p.m at the coast of Alaska, where below the Antarctic circle we know there is always daylight at those times, which can and has been observed. With this FE model, the entire state of Alaska should be in complete darkness at Noon. The sun is actually closer to these locations at midnight.