No, they don't increase the amount of hp being transferred. Transferred power remains the same too. That power appears to increase is an artifact of that type of dynamometer which doesn't normally take into account differences in wheel/drivetrain inertia between one run and another. Ideally, the operator should input different drivetrain inertia values after changing wheels (or the flywheel) but that is seldom done for either incompetence or lack of data.
Hence, the myth that lighter wheels increase wheel hp.
This is the same situation that there's with "software dynamometers" (not done on rollers, but on open roads, usually via OBD) where you have to input, among other data, the correct car weight. If you remove weight from your car without updating the car weight in the software, the output will apparently show an increase of wheel power. Such software typically works with inertia-based algorithms too, by the way.