If you look at line 762 of 'ArduCam_ESP8266_FileCapture.ino' you should see it is looking to read two bytes from the camera to check that the model number is either a '2641' or '2642'.
You are seeing the error because you are not getting those values back. So between 761 and 762 insert some debug and print what you are getting back:
Serial.print ("vid = ");
Serial.print ("pid = ");
I guess you will either get 00 00 or a different valid (maybe) model number. If you think its a valid model number add another condition to the if statement and see if it works.
Oh and don't forget to post the results, because I'm going to give it a chance too when I get time :)