Nope, you've got it exactly right!
http://upload.wikimedia.org/wikipedi...m_of_water.svg
Here is a typical Pressure vs. Temperature diagram for water. What we're used to seeing in thermo is Temperature versus Specific Enthalpy or Pressure versus Specific Enthalpy with constant Pressure curves drawn across the former and constant Temperature curves drawn across the latter. On a water P v h or T v h diagram you would see a "vapor dome" where basically you maintain a constant temperature until all of your liquid has boiled or all of your vapor has condensed.
Anyways, when playing around with temperature and pressure you reach the "Triple Point" where all three phases of matter simultaneously exist. The reason you are seeing the matter in the video go from solid to liquid to gas and back again is because the temperature and pressure combination inside the pressure vessel is likely dancing around the triple point.
This concept seems unreal to us because we're used to the more terrestrial 1 bar (red horizontal line in the graph above) pressure zone where we're used to seeing ice and water together or water and vapor together but never all three simultaneously. As you see in the graph above, drop the pressure down to about 1/100th of an Earth atmosphere and hit 0C and magic starts to happen!
Actually, I've never seen a video of this recorded before so thanks for sharing!