Allen, is this the video you were talking about? The URL you provided was to the video uploads page for broaudio, not to a video it self.
In this video, he is seemingly cooling both sides of the TEG. These devices work on therm differences, one side cool and one side hot. I am not sure why he is putting a heat sink on both sides, unless the stove is just to hot and is damaging the device. In that case, it wouldn't be an improvement to find additional heat to be extracted from a stove as the device is already at its heat capacity. What you could do is build a smaller stove that has much more focused heat spot but still burns efficiently.