I can't watch the video as I'm on mobile, but I'd imagine they've just got a coolant loop that runs through a compressor to chill the coolant?
That makes for an interesting science experiment, but compressors are large, noisy, and very inefficient. If active cooling is what you're after, you'd want to use a peltier cooler, which is basically a metal and ceramic plate that passes a DC current through a substrate. This cools one side (easily below freezing point) and heats the other, which you can then cool with a traditional water loop.
IIRC, there was at least one PC company that sold custom builds with that sort of system. They were impressive insofar that you could literally have massively overclocked parts that ran continuously at zero degrees, but the systems were both wildly expensive and wildly impractical since you'd have to figure out how to avoid condensation and other problems.
As far as I know, these have basically fallen away as power consumption of parts has dropped.