Earlier, Kingdom Hearts -HD 1.5 ReMIX- was announced at Tokyo Game Show 2012 with a new trailer. Square Enix have uploaded the trailer to their official website for the game, and you can watch this new trailer in HD 720p at the link below.
One small notable detail is that in the Kingdom Hearts Final Mix remaster, the 4th command slot (which is used for opening chests, examining things, special abilities, etc), has been changed into a triangle-button "Reaction Command" like Kingdom Hearts II. You can see this below.
Update 3: Our partner on YouTube, Everglow8444, has created an unofficial English version of this trailer, using the voice acting from the English versions of the games. You can see this below.