Apparently booking a hotel room and then failing to produce the credit card when you check in is a problem and the hotel should have told you that they needed the physical card there to charge the room.
I’m going to murder someone.
They typically say this in the email that has your room reservation. For example:
The first night’s deposit is fully refundable provided notice of cancellation is received by Room Reservations at 800-288-1000 at least 48 hours prior to arrival. If you are paying by credit card, you must present the credit card at check-in. If you are not the credit card holder, please contact Room Reservations for details on our credit card policy.