I'm playing around with the Unity runtime and it works fine for Spineboy, the goblin and the powerup examples when I export them as JSON from Spine and generate an atlas using Texturepacker in LibGDX format.
For some reason the dragon example doesn't work in Unity though. There's no error message, it just shows up completely garbled, as if it reading the wrong areas from the texture atlas:

When I play the animation in Unity the movement looks similar to what I see in Spine, except for the wrong textures.
I'm using the same Texturepacker settings as I did for the other examples, so I'm not sure what the problem could be that's specific to the dragon?