The key card for a Model 3 is just an RFID (Radio Frequency Identification) prox card, like you might use to enter an office building. The video shows an iPhone being placed where you would set down the key card.
Apple Pay uses NFC (Near Field Communication)/RFID to talk to payment terminals. Any time an iPhone with Apple Pay sees an RFID terminal, it assumes that it's available for payment. In this case, it assumed wrong. If you actually were to scan your fingerprint, the iPhone would just sit there saying to "Hold Near Reader". The car won't take your money.