Do American Express cards have a similar authentication?

For American cards, the 'extra level of authentication' will work slightly differently. Amex uses the AVS-Address Verification System.

On the payment page of BookMyShow, you will be asked to enter your billing pin code. This will be checked against your card statement the bank has on its records.

If the pin code doesn't match then your payment will be rejected. If you have difficulty in recollecting the exact billing pin code, please go ahead and confirm it from your Credit Card statement.

PS: You can use American Express for all the cinemas except for Scope Cinema.