Wow...

Well, if I need to guess, I'd say:

• multiple meshes (see how many slots there are...)
• gradual translation+scaling from/to zero for the "turning" parts
• resorting and/or disabling of the parts on the back when needed
• amazing level of skill and patience

It's really impressive.

fwiw here's their original showcase post: Fully rotate 3d in Spine 2d

And the diamond blog post that seems to have sparked the idea:
Blog: Rotating diamond tutorial