Ok, while also seeing all the bullshit in the Solus campaign, I do think it can make heating more economical. By emitting a large portion of the heat as IR, it can give away heat faster - note, not more efficient, just faster. Meaning it warms up the same with the same power, but cools down faster. It has less thermal mass. So if your goal is then to get your small room up to a predefined temperature, you can turn off the radiator sooner. With traditional oil radiators, you'd turn off the radiator once you've reached your target temperature, at which point your radiator has still a lot of heat stored, so in the end you're going to over-heat your room and you've needlessly wasted electric power. If you have less "thermal mass" in the radiator, you can get away with less redundant heating, hence being "more efficient" (economically, not physically).
I'm pretty sure this is the theory behind Solus, but of course any decent PID regulator could take care of the above problem even with traditional oil radiators. The problem is: most mobile radiators don't come with one. Most don't even come with a regulator at all (just a static power level knob), and those that do, do simple target-temperature-threshold switching and have no PID control. Solus, being a low-thermal-mass radiator, could probably create a more accurately working PID regulator for it, and that is where the operating-cost advantage should come from.
How much saving that actually amounts to? Dunno, but 80% seems way too much for me, that part is probably just BS again. Not even mentioning that IR heat won't heat air up (at least not directly).