To me it actually looks like the combat is NOT action combat, but a variation of the classic FF ATB system cleverly disguised as action combat.
The blue bars seem like they are an ATB bar that is split into different "slots" for commands, much like FFXIII's ATB bar. These probably recharge over time, or as the characters use normal attacks.
If you look at the shortcut menu, you can see there's a possibility to switch to other characters, and their available ATB bar slots are also shown. So you can e.g. switch to Barret and use his commands, until his ATB bar is fully used up, while you wait for Cloud's ATB bar to recharge... which is exactly how the original game worked.
So if you're into that, you can play the game in a classic ATB/turn-based FF way.
The major new combat element here is that you can also hit enemies while your ATB bar is depleted - but then you only have access to the normal combos and "punisher" attacks, both of which most likely do less damage than the special command attacks, but they do help to replete the ATB bar faster (or at least to kill time until the ATB bar is full).
So you're still waiting for ATB bars to charge, but the waiting is more fun because you retain control of your character and can do some slightly weaker attacks in-between, and by using the ATB slots individually you can manage just how much of the ATB bar needs to recharge. So while you can play it in the classic way, it can also be much faster and you have things to do while waiting, making it feel like action combat as well.