Is there technical reasoning behind Animoji being exclusive to iPhone X? To what extent, if any, is Animoji dependent on the camera and sensor system specific to iPhone X? Would there be a noticeable quality difference if the Animoji software was available on other iPhones?
My understanding is that Animoji requires ARKit. Since the iPhone 8 and 8 Plus rear camera supports this, it could be possible in theory to use these cameras to create Animoji. However, using a rear camera would be problematic at best, since you wouldn't be able to see yourself as you're creating the Animoji. And since ARKit is not supported on any front facing camera except for the one on the iPhone X, it is further problematic using the software on any other current model of iPhone.

It's also possible that since Face ID itself is not required while you're creating the Animoji, that the process may still use the map of your face initially created by Face ID when it's set up (this is pure speculation on my behalf). If that is the case, then creating Animoji on an iPhone 8 / 8 Plus would not be possible - at least not to the quality we see on the iPhone X.