Is an air gap required for our new Kinetico water softener?
This may be a little late for you, given the question is some months old, however...

I have a Kinetico Premier Compact softener installed by the main water entry to the house.
It was installed about seven months ago by the local Kinetico distributor.

The drain tube does go to an air gap under the kitchen sink.  

The installation manual states that this should be done, as shown here