There is no way to tell what product is on the floor. Uniblack 1 is a good guess, but unless you get confirmation from the person that applied it, it's only a guess. It could be a dye, or any number of or enhancers. If it is only the color that is affected, then the sheen on the stone will be uninterrupted across the damaged areas. If this is the case, then follow Rob's advice
If the sheen is gone from those areas, then it is etched as well and will need to be refinished with antiquing brushes. not many people are equipped to take this on in a house.