Both times I watched the trailer, the battle system made me think it went like this:

Your characters' ATB bars begin filled and the battle is paused (like it is when you input commands in Wait mode in FFXII), you input a chain of commands and press a button to resume action. All characters and enemies execute their chain of commands until their ATB bar runs out or the chain of commands is exhausted. As soon as one character is out of commands or has no ATB the battle stops again for that character(s) to create a new chain with a newly refilled ATB bar. Of course, when an enemy runs out, they'll automatically be refilled/be given new commands without the battle stopping because no human interaction is needed for this to happen and the battle continues as normal.

Of course, I doubt this is how the battle system works, but I think it's rather neat.