Legally speaking it shouldn't be Godzilla, because Toho retired the franchise. Also the US rights are heavily disputed, its with either ColumbiaTristar, or Sony where 1-18-08 is Paramount. That and Abrams himself said the monster was totally original.
From the shots that float around on 1-18-08 it seems like thats the real title, since the movie apparently takes place on that day. So the film is probably just the one night with the friends of the party fleeing and hiding, like War of the Worlds.
As much as I don't believe its Godzilla I did notice that in this .gif you can see almost the Heisei Versions exact silhouette in the cloud of dust.
