Both processes create/release heat, and in Alec's tests in the linked video the bulk of the heat from the dehumidifier running in a humid space is coming from latent heat released from the water. That may not be true in regular operating conditions, but there will always be a substantial amount of heat released from the water when you trigger a phase shift.

> I don't think there has to be any heat involved with collecting water molecules in the air into a larger volume of water, depending on the process used.

The only other option is to increase the pressure in the room or in a space within the room, which this material pretty clearly isn't doing.