During the landing flare in a twin-engine airplane, the 1,391-hour commercial pilot heard the landing gear warning horn. The pilot stated that he added engine power to initiate a go-around as he extended the landing gear. The airplane's propellers struck the runway and the airplane skidded approximately 650-feet down the runway before coming to a stop on the runway. The pilot egressed, uninjured, through the left cabin door. The throttles were found in the "full forward" position and the landing gear selector handle was found in the "down" position. The inboard main gear doors were found in the retracted position indicating that gear sequencing had not started when the airplane touched-down on the runway. Company policy directed the pilot to extend the landing gear prior to descending below 1,000-feet above ground level on approach.