As I recall, the traditional AMEX card isn't a credit card. They expect payment in full. But to appease customers who didn't wish to pay for large purchases in full they have this facility to pay installments. This also allows them to make buckets of money as this facility comes at a cost.
The old universal paper charge card forms had a box where one could choose this scheme, but was only valid for AMEX (and possibly Diners?).
Nothing new under the sun ...