What you are seeing is dust that is being transferred from the floor to the counter top. I know, because I had a little soot on my basement floor, near the oil furnace from some downdrafts etc. and I had black paw prints on my light colored counter. As Jay said, there is no way to seal or treat the countertop. The reason it shows dirt is because it is black. Black cars show dirt and dust too, you just have to keep cleaning them. I prefer colors that are more in the middle of absolute white or black. You could try vacuuming more to reduce general dust levels.
Also, is there a particularly dusty area somewhere in your house that the cats are walking through and tracking it into the kitchen? If there are dirty or dusty parts of your basement or attic etc. then either keep them cleaner or keep the doors closed so the cats can't go in there and then track it everywhere else.