The pilot reported that he was inbound to the airport when he heard that another airplane was also approaching the airport. The pilot of the other airplane intended to enter the downwind for the same runway, so the pilot opted to do a straight in final approach. When the pilot initially intended to lower the landing gear, he realized the airplane was too fast, so he did not lower the landing gear at that time. Then, he heard the pilot of the other airplane make a radio call and he became distracted looking for the other airplane. As he approached the runway, he heard a horn, but he assumed it was the stall warning horn. He stated that he was not worried about the warning horn because the airplane was already positioned to land on the runway. The airplane then landed with the landing gear retracted. The lower fuselage structure was substantially damaged during the wheels-up landing. After the landing, the pilot realized the horn he heard was the landing gear warning horn and not the stall warning horn. He also said that he erroneously thought he lowered the gear down lever before landing, but it was the flap lever that he manipulated instead. The pilot acknowledged that he should have reviewed the Before Landing checklist before he entered the traffic pattern. The pilot reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation.