It is actually both of their problems. HDFC most likely didn't incl its paytm co-branded cards to be incl in their agreement with amazon for hdfc card offers & amazon didn't ask for it either as very few ppl actually use this card on amazon.
It is not because of co-branded but because of competing co-brands. Amazon/fk/tata/paytm all are competing against each other in ecomm segment. Why would a platform want to promote their competitor's brand on their platform? On the other hand, take icici makemytrip card which works on all ecomm sites for all icici card offers because makemytrip isn't competing in ecomm segment.