A Secure Offline Bitcoin Payment System
How does the transfer between the payer and payee's wallet actually happen if both nodes are offline? 


From the paper:


  Because both, the payerX and the payeeY, have no on-line connection during the payment, the offline transaction τo is sent via local interfaces (e.g., Near Field Communication (NFC) or Bluetooth Low Energy (LTE)), in contrast to regular (online) Bitcoin transactions which are transferred via the Bitcoin peer-to-peer network.


So basically, whatever way the two devices can communicate will work just fine to communicate the transaction.


  Does the offline wallet operate as a Layer 2 protocol somewhat allowing for deferred settlement like LN?


I would not say it is analogous to LN, the function and trust model is different. From the paper:


  These  mechanisms achieve probabilistic security to guarantee that the attack probability is lower than the desired threshold.