Airport security video showed the airplane land and taxi to the self-serve fuel tank. The pilot fueled the airplane, but he did not put the left fuel cap back on or closed the fuel door after the fueling was complete. The pilot then pushed the airplane back about 15 ft, boarded the airplane, and started the engine with no preflight inspection observed on the video. As soon as the engine started, the video showed the left fuel cap falling off the back of the wing. The airplane then started to taxi, and the unsecured fuel door on top of the wing could be seen flopping up. The security video then showed the airplane taxi back to runway 15 and depart. The video did not show the airplane after departure.