I need help with animation.

Ha, what a fun idea! I can't think of any reason why it wouldn't work. Can I check out the file? 

http://pasteall.org/blend/

Ok this is a good challenge! Intuitively it seems like it should work, but there's a catch. 

First, apply scale to make things more stable. 

Then for the animated domino switch to the Convex Hull collision shape and make sure it's set to Final so that the collider is the shape of the deformed mesh. 

If you play back the animation it still stops, but notice the location and rotation of the domino if you turn off the armature modifier at the end. It's standing still! Rigid Body physics uses the object origin location and rotation to calculate everything, and while it's taking the deformations into account the actual movement is not contributing to the motion vector. 

Try this:

1. Keep the armature modifier but remove it as the parent of the domino. Instead, make the domino the parent of the rig. 
2. Keep the squash and stretch deformations, but mute the animation of the root bone. Just un-check it in the dope sheet. 
3. Now animate the location and rotation of the domino instead of the root bone. That should give the rigid body sim the information it needs to take it from there! 

Bummer! Yeah that does need to be centered, I forgot that part of the puzzle. Good luck! If you pull it off it'll be the best start to a domino animation I've gotten yet ✌