That is a really beautiful floor with a really high shine.
Not sure but if you really need to know the name of the stone I'd bet that Stu Rosen at mb stone could Id it for you.
It looks like it is in great shape, it actually looks like was just restored or very well maintained.
The more I look at those pics, the more I'm thinking granite. Quartz will give a sharper, more "sparkly" type of geode-pocket formation, whereas onyx would have more smooth ripples of color like waves. Looks awfully similar to what he's got on those countertops, too.
A Moh's hardness test and / or a few drops of acid in an inconspicuous place would help distinguish between granite and most other stone flooring.
Granite is the hardest stone commonly used for flooring. Quartz is 7. Onyx is around 6.5 . Granite is between 8 and 9. Marble, limestone, travertine will all be near 4 or 4.5. A steel nail is 5.5. It can scratch softer stones but not higher numbered (harder) stone. You can also get a set of stones to test for Moh's hardness.
This house was donated by a wealthy individual to a local charity. I have been contracted to do a complete clean up of the entire inside and outside for the tile, bathrooms, kitchen countertops, pressure washing, roof cleaning, window cleaning, hardwood restore and anything else I recommend. The closer I look at this home the more amazing I find it. I'll relate more later after I get this floor ID'd.