For instance: http://www.youtube.com/watch?v=j3w5XMJVuok

It's not the best example (it's a mashup and not a preview, but the concept remains the same), the music probably actually hurts it more then it helps it (which SE wouldn't even be able to go down this path to begin with), but it's far more engaging then anything SE has put out. On top of that, it does give prudent information about what the fight is about. It's not just all about being "flashy".

We understand that there are multiple moogles, we understand that each moogle has its own job which one can assume that each moogle has their own set of unique abilities, there is a main large moogle, we are in an arena, we even get some back story prior to the actual engagement, etc. It gives everything that SE gives, but with a far better direction and scope.

It's more then just showing auto-attack.

Again, it was fan made, there are dead spots in the video where it just drags on and so forth but it's a great example imo that even taking some time to edit a video can make it far more appealing.