If you’re trying to convert energy (fuel, electricity) to heat, then the heat pump is the way to go. The guys in the video were unclear of the concept, but electric resistive heating is, technically, completely inefficient–all of the energy is converted to heat, none to work. A heat pump might be 66% efficient–that means you get 3 units of heat pumped per unit of input energy. AND, you get another unit of heat, because the inefficiency ALSO generates heat. That’s if you are pumping heat out of the cold outside air into the car. Of course if you’re pumping heat out of the car into the hot outside air, then the efficiency reflects only the heat pumped out–extra warming of the outside hot air doesn’t count.
In an electric car, a heat pump is clearly ~3X or so more efficient than resistive heating (like a home heat pump, the efficiency depends a lot on the ambient conditions). Air conditioning always uses a heat pump, in any car (but the system isn’t reversible to provide heat in most of them). But, the caveat IMO is that heat from an IC engine is readily available and otherwise wasted. I suppose this might not be true with super-efficient turbos, but not so for the XK. Similarly, mechanical power is available to operate the compressor. There are certain advantages to having an electrically powered compressor (constant speed for example) but to get the electricity you need an alternator, which isn’t constant speed (except on a diesel-electric train) and therefore isn’t very efficient. But generally, an all-electric heat pump is impractical in a non-electric car.
I suppose one could have a “hybid” car where the XK engine provides motile power whilst a rechargeable battery pack powers a heat pump. IMHO.