Anyone who has tried to mop a non-slip floor with a standard mop would know how hard it is. Not only pulling the mop around but also leaving half the mop there as the aggressive surface tears the mop head to shreds.
I have found that the Microfiber mop heads are better for these surfaces though do tend to hold more water and feel heavier to use.
Even better is the Fluid Flat Mop System which allows you to get under shelving.
Either way, the floors need to be cleaned well, especially in commercial kitchens.
We recently cleaned this commercial kitchen that has catered for over 400 people in multiple sittings with our Wizzard floor scrubber.
This kitchen is well maintained daily but you can see what an occasional run-over with a scrubber can do.