Specifically, what the heat pump dryer is doing is basically pulling air through the clothing which evaporates some water from the clothes into the air, then cooling the air, which causes water to condense, removing the condensed water and warming the air back up to send through the clothes again. The effect is much closer to the clothes hanging from a line in a garden on a perfect drying day, except it's inside a box.

Whereas the other way to do this is just cook the clothes and the water evaporates, then you dump the warm moist air either outside or into a separate dehumidifier which throws much of the energy away. As you observed this is faster, but most people don't need faster if it's unattended. My dishwasher is slower than washing dishes by hand, but I don't need to sit there watching while it does it so who cares?

My heat pump dryer doesn't vent and captures the water to a tank or pumps it down the drain.