The pilot reported that he retracted the landing gear following an aborted landing due to traffic on the active runway. He stated that on his second approach he carried power due to the gusty wind condition, but during the landing flare he realized that he had failed to extend the landing gear. The pilot further said that after he realized that the landing gear was not extended he added full power; however, the airplane impacted the runway with the landing gear in the retracted position. He added that he did not follow the checklist and that he did not hear the landing gear warning horn during his approach. When informed that the throttle position to activate the landing gear warning horn was only about one-half inch beyond the full aft idle position, the pilot indicated that he had not retarded the throttle that far. The airplane sustained substantial damage to its undercarriage as a result of the abnormal runway contact.