SMS Relay – Hardware requirements?
I think you are confusing this with the requirement for Bluetooth LE to be able to do Handoff.

SMS Relay uses Wi-Fi or, if available, your phone's 3G/4G connection.

From How to Enable SMS Relay on Your Mac, iPad and iPhone - point 3 might be the salient one...


  
  Make sure your Mac, iPad and iPhone are all connected to the same Wi-Fi connection.  
  Make sure all of the devices are logged-in to the same iCloud account.
  You don’t want to be receiving your father’s phone calls, do you?  
  Starting with your iPhone first – and this is important, because I did it backwards and messed everything up – open Settings > Messages and tap “Text Message Forwarding.”  
  Choose the devices on your home network that you’d like to receive SMS messages on – in this case, I chose my MacBook Air and my iPad.  
  You should receive a code on your iMac and iPad.  
  Enter that code into the prompt on your iPhone.  
  


This might also be useful - FYI...SMS Forwarding does not require WiFi to work