The radioactive material in this case is contained within the tungsten ball. It would emit few harmful radiations, as the metal absorbs them and converts them

The radioactive material in this case is contained within the tungsten ball. It would emit few harmful radiations, as the metal absorbs them and converts them to heat, but most importantly it would leave no radioactive isotopes behind since these byproducts stay in the ball. As the ball approaches the core, the tungsten would finally start melting, and what remains of the radioactive elements would be released deep in the mantle. In fact, as the paper mentioned, this has been proposed as a way to safely dispose of nuclear waste material.