You only looked at the second video and were the heat is taken from the system. The TWO video links show the concept of thermo siphon, no mechanical moving parts, so no electricity needed for system to work. You will not freeze if you do not have POWER, like in a winter storm, as long as your water did not freeze because water is your heat storage median. The heat is siphon off the top the barrel in this rocket fireplace and you only need to load it once an hour, unlike a 6" system 15 minutes, that this rocket fireplace replace. The author of this video did a concept build and and state that he would build a 16 in feed system next time with 25 feets 1/2 cooper coil to get better heat transfer from the to of the barrel. Here is the video link for the coil at the top of the barrel being build.
Part 4 of the build. The working thermo siphon is in part 7