This edition of the movie is actually The Godfather: The Coppola Restoration which began in 2006 as a project to restore the movie using the best source materials that could be found
Noted archivist Robert A. Harris worked with the original cinematographer, Gordon Willis, to create a reference edition of the movie that matched the original frame-by-frame. Their efforts on the first movie, as well as The Godfather: Part II, were released for home video on DVD and Blu-ray in September 2008. (The Godfather: Part III was also released in that set, but it did not require the extensive restoration work of the other two)
The press release from Cinemark labeled this event as showing the "The Coppola Restoration of “The Godfather” 40th Anniversary Edition" but it does not appear to be any different than the version that was released on home video back in 2008.