1. A keyword extracting device, comprising: an audio input section that inputs speech sound of a first speaker and a second speaker, wherein at least a start of the speech sound of the first speaker precedes a start of the speech sound of the second speaker, and the speech sound of the first and second speakers includes speech sound of a preceding speech and speech sound of a subsequent speech; a speech segment determination section that determines respective first and second speech segments respectively corresponding to the first and second speakers in connection with the speech sound so as to separately identify speech sound from the first and second speakers; a speech recognition section that recognizes respective speech sounds of the respective first and second speech segments determined for the first and second speakers; a speech response feature extraction section that detects a speech response feature only from the second speech segment corresponding to the second speaker, the speech response feature indicates a presence of a keyword in the first speech segment corresponding to the first speaker based on the second speech segment as a response to the first speech segment of the first speaker; and a keyword extraction section that extracts the keyword from the first speech segment specified by the speech response feature detected by the speech response feature extraction section, wherein the keyword extraction section extracts, as the keyword, a constituent element at the end of the first speech segment corresponding to the preceding speech prior to the speech response.