Amazon only requires id when you order from Amazon Global, and that's because customs requires Indians to provide identity and address proof when you're importing something. If you don't want to provide it to Amazon, you have the option of providing it to the courier service (FedEx/Aramex/whatever). Also, you can provide any other address proof like driving license, electricity bill, voter id etc. Aadhaar is convenient because it is one of the few documents that are accepted as proof of both identity and address (passport, driving license, voter id and ration card are the others).
So, yes, clickbait article.