I have similar tile except lighter in color. The "dings" do not fill with dirt. My house cleaning service mops it every 2 weeks. We do not have children at home, nor do we have pets, so, we don't get dirt tracked into the house.

However, when I had the kitchen remodeled, I had to have some extra tile laid (I had initially bought extra because I knew the remodel was coming). The tile guy who laid the first tile did not get grout in the dings. The tile guy who laid the extra tile did. I have not been able to get that out. Make sure you clearly instruct your tile setter to thoroughly clean all of the dings, then closely inspect his work as soon as you can get on the tile.

We have similar tiles on a table outside. All it takes is a little soap and water with a brush to clean and that is after being outside for months. Easy peasy.

We have that type tile and the little dents have never filled with dirt.