Can be tricky to say for sure what something is without seeing it in person. The pictures definitely look to me like a highly polished marble. Done right, polished stone can a 3D appearance. I've had to get right down on the floor to tell for sure if it's polished stone or stone with a high gloss finish on top. Some spot testing may be needed to determine for sure.
It could also be porcelain (some of the porcelain tiles can be pretty hard to tell the difference) but it wouldn't be polished. The gloss on porcelain comes from the glaze or from a topical high gloss finish being put on, which you shouldn't do.
If it has a finish, a little drop of floor stripper in an inconspicuous area will start to remove the finish. If it's marble, a drop of acid will etch the stone.