You see in the video, Louiseux protects you with a sphere, and they mention sending you to a different place/time, hence why we are still alive in what is probably a distant future post Garlean destruction. In the final CS, Cid mentions that we have stopped Dalamud in its tracks, and its progress towards Eorzea was solely based on Nael deus Darnus. Because of this, Louiseux won't need to do his final plan/solution.
Actual chat:
Cid: The how of it is beyond my fathoming, but it seems the White Raven sought to draw Dalamud unto himself.
Cid: To this end, he raised the floating isle...only for you to send it─and his hopes─crashing to the ground.
Cid: Which leaves Dalamud short of an earthly sanctuary, and condemned to hang in the sky where it bloody well belongs.
Cid: Sounds simple enough in retrospect, but I must confess, my heart was in my mouth throughout. Seems I needn't have worried, eh?
Cid: And with matters resolved, we won't be requiring the “last resort” old Louisoix kept muttering about...whatever the hells that might have been.
So it would seem that, in the future, the Garleans somehow continue with their plans and Louisoix must indeed enact his last resort, and we return to a whole new world cue the alladin song.