Ah I had no idea these were all ventless with no option for vented, but I guess it makes sense.
Here is a study meta analysis that actually goes into some minor detail about the process. The main advantage is capturing some of the heat out of the waste stream and recycling it in the process. Hybrid heat pump dryers with standard electric heating elements along with the heat pump came out to be the most efficient. The median payback period on the energy savings from one study mentioned was 22.1 years. The one trick they seem to miss as far as I can see - they did not compare them to unvented operation of standard electric dryers where the process heat is also recaptured at basically 100%. The bonus over a standard dryer in that case would be very low, most likely zero. Since most people only operate dryers that way in the winter, it would at least have a part-year efficiency bonus in most installations.
Heat pumps in unvented space/appliances don't make heat more efficiently than a simple heating element in an unvented appliance of course, and that's always the rub... Your just stealing exact same quantity of lower quality heat out of the room, increasing the energy quality temporarily for a constrained high entropy process, where the entropy of the compressor is also useful to the process. It takes the exact same amount of energy to evaporate the water out of the clothes, no matter how you spin it (heh heh) - all that matters is how much energy is wasted to the exterior of the process/building/etc. The energy state in any unvented appliance install where heat/energy does not exit the main containment vessel (home/reservoir) will always be at equilibrium.