I think that credit card includes both memory (encrypted, or something) and chip-processor-CPU. It just needs power source to start working, and somebody to communicate with. In this case, gizmo is power source, and somebody who knows credit-card language well enough to conduct card's communication with the bank through the computer.

NFC of your phone can act as power source (beware of battery drain) if your card supports contact-less payments, but the communication API (imitation of gizmo) will be the most troublesome part. Because bank will likely try to keep it a secret.

Oh, and I forgot: if credit card designers are paranoic, the contact-less aka NFC communications will be more limited than contact-communications. A different algorithm for them, or something.

Thank you. Best wishes.