What IS a 'Thermal Siphon' system, if it's possible to explain in short and lay terms?
It's a phase change heat transfer device that works on a similar principle to heat pipes and a vapour chamber. Where the heat source (the processor in this case) boils a liquid (in this case water under negative barometric pressure and dosed to reduce the boiling point). The vapour travels up to the heat sink (in this case the radiator) where heat is exchanged with air blown over the finned surface. The condensing fluid falls under gravity back down to the heat source.
The biggest difference between heat pipes/vapour chamber and a thermosyphon is the way the condensed liquid returns to the heat source. In a Thermosyphon it's by gravity. In heat pipes/vapour chamber it's through a porous wick via capillary action (i.e. the same principle by which water travels up a piece of toilet paper when you dip one end in water).
The issue with Thermosyphons is that they need to be carefully designed with a large enough diameter in the tubing to avoid surface tension effects overcoming the force of gravity; thus reducing efficiency, as well as having limitations in their operating orientation. For a thermosyphon, because it relies on gravity, the heat sink needs to be located vertically above the heat source, otherwise there would be no hydro-static pressure to push the liquid back to the heat source.
Also, as with all phase-change devices, if the heat source fails to remain sufficiently fully wetted during operation, film boiling can occur; which is where a thin film of vapour sits over the metal connected to the heat source, providing a barrier to heat transfer and allowing the heat source temperature to rise well above the boiling point of the liquid. Given that thermosyphons rely on gravity to the return the liquid, this is a much bigger problem for them than for heat pipes/vapour chambers.
I think thermosyphons also require much larger heat fluxes for them to operate efficiently. So I would presume for a consoles they would be out of the question, unless the console APUs are pushing 250 to 300 watts (and even then the thermosyphon cooler would need to be very carefully designed).