Well, as far as I read from the offical page. It didn't say anything about is being a Fan Disc like the one before with Mai and Arika in it. Also, I didn't see the word FAKE.... unless my Japanese skills had gone down the toilet big time... then again, I'm not good with katakana to begin with
毎回映像特典： 舞衣が！なつきが！命が！そして、アリカが！！幻の劇場版『風華大戦 舞-HiME THE MOVIE』予告
Although, I don't know if this movie will air in the theaters. I mean, it clearing says,
Each time speical video: Mai! Natsuki! Mikoto! And then, Arika! Theater Vision『Fuuka Taisen Mai-HiME THE MOVIE』Preview
So this might mean that, the staffs of Sunrise might make this movie and might not.... so....