That is a really stupid law if it is true. A gift card is an anonymous payment method. It is more private than using Bitcoin in most circumstances. Does that mean that Amazon is going to start KYCing customers who pay with gift cards?
My impression is that the AML/KYC requirements kick in when money -- including bitcoin -- is exchanged for gift cards, not when gift cards are redeemed at the issuer.
Regardless, Amazon has already begun requiring KYC for gift card redemption, although I think it's for fraud and loss prevention more so than money transmission law. You need a linked credit card or bank account (and in the US a verified address), otherwise your account is likely to be locked after gift card redemption. Notice the warnings that Bitrefill now posts on its Amazon gift card pages: