I can't wait for the other finishing moves. I hope there are some good finishing moves involving sword and shield!

No, but the hit needs to be strong enough that it would be an insta-kill. So if a regular backstab wouldn't kill them, you'd need to do a power attack to see the animation.

I am trying not to be repetitive here, but here is how I get that animation ~98% of the time. (70% of my statistics are made up on the spot)
1. I use my dagger (now improved to legendary, but it worked before) without anything equipped to the recessive hand (but it still works sometimes with a shield in one hand, and even with a sword)
2. I sneak up as close as I can and stand still (again, not necessary but seems to increase chances)
3. I do NOT use a power attack if I think the enemy is weak (still works at times when using a power attack, but not nearly as often) - has to be a one hit kill

To be noted, my sneak skill is 100 but I think it started working around 40, and I have the perk where daggers do 15x damage. And nearby NPCs have nothing to do with it, but you cannot be spotted by the victim as you are attacking, or it won't work.