I think you left out some salient words: upto 38% off
Also if this is like other Amex discount fares it is a discount off an inflated fare and so does not really save you anything, and in particular if you hunt around fora discount J fare. The saving kicks in more if you were in the position of having to buy a late full priced fare.
A quick google revealed this reference from 2014 on Flyertalk:
New Zealand AMEX Platinum Charge Card benefits?
What is included in the Airline Privileges Programme
To answer OPs specific questions:
Airline Privileges Program - at the time it was access to companion airfares on NZ, EK and SQ (maybe QF - I don't remember). It did have some value, but you had to buy full C fares on NZ and if discount fares were available it didn't work out. On the other hand, if C fares were all that was available then it did work nicely. Since then the AU and other Platinum cards have been extended to offer "deals" for single travelers as well, but I've never found them particularly useful (ex-AU there were some decent WTP deals on BA for a while).