No idea how the Lennox units in TFA do it, but the Mitsubishi "hyper-heat" units do it by diverting a small amount of their output back into heating up the refrigerant at very cold temperatures. It starts to get a bit "slushy" at the low end of the performance range, which impacts the ability to move heat. By warming it back up to the bottom of its ideal operating range, the whole system functions more efficiently.
It can operate efficiently at lower temps. Current air source heat pumps see degraded performance and below freezing temps and will not be able to effectively heat a home at the lowest temps that can occur in the northern hemisphere.
The "secret sauce" of the increased efficiency is that they're using thermoacoustics, which previously had been a technology used in one-off applications with a large budget (e.g. the James Webb telescope uses it to stay cool). Prior to now there were no manufacturers providing the technology to be widely available at scale.