"Kindly note that Credit Card holder must be traveling with the passenger and should present the Credit Card used to purchase the ticket(s) at the check-in counter for verification. Royal Jordanian reserves that right to deny boarding any passenger who fails to represent the Credit Card used to purchase his ticket."

My interpretation of this is that I had better have my credit card with me, or I might not get on the plane. Pretty simple to me. That's how I read it.