If I had to guess, the animated point cloud isn't tasked with transferring lots of (megabytes) data, but is probably a proprietary version of a QR code, both for aesthetics and security through obscurity. Its format may also have higher information density than a QR code, which would work well for encrypted data.

I imagine the heavy lifting is done on Apple's server. The data being transferred locally is likely a GUID/IMEI/etc + a nonce.