I have a few observations to make about seeing the Death Spell in action. First off, I believe the way you use it is actually channeling the cast with the Attack button and using the left-analog stick in a specific direction to chose between various spells. The reason I say this, is if you look at the video in certain areas you will see the ring glow a blueish white color until Death starts casting and it turns into the purple red color. I believe that this is how you will get multiple spells out of the ring, similar to how holding backwards on a broadsword can use Tempest or Heavy Thrust on a spear.
Something else I noticed that I saw someone on Twitter point out as well, was Noctis did a creepy laugh at one point in the video while using Death. Not only that, it seems that while using death the edges of the screen have a creeping black effect and it starts to consume the corners. Not only that, but it stays after you use the Death spell as well. I wonder if this has something to do with the price you pay when using Death. Why else would they leave the dark edges of the screen after you use the spell? And, why would Noctis have a creepy laugh? The edges of the screen do seem to return to normal after you finish the battle you're in though.
Perhaps the Death spell has some negative effects over Noctis' consciousness and he can be consumed by darkness and maybe even resulting in a game over or some weird state?