Well it's two-pronged right? They either keep their extra houses and pay the tax, which increases tax revenue which can be used to fund things like constructing housing in NY, or they sell them off. The people potentially buying these houses will be more hesitant themselves to buy, so they're forced to lower the sell prices, making the houses more available to the general public.

I guess three-pronged, cause it says if they turn it into a rental that it's exempt from the taxes, which means someone is still at least living in it rather than just being used as a speculative asset.