I would imagine it is just like clear vinyl windows some convertible tops that turn "yellow" in time due to the UV breakdown of the vinyl plastic "structure" (chemical make-up) that caused it to loose its opacity (clarity in allowing light through it). Now WHY it exactly happens in chemical terms is beyond my scientific understanding and how to prevent it, I assume, is more the "grade" of the vinyl used in making such mats.
Never tried a plastic cleaner like Meg`s Professional Mirror Glaze No.17 Plastic Cleaner or Novus No.2 Plastic Cleaner because:
1) Its a large area to apply to, meaning it would use a lot of cleaner,
2) It is not a smooth surface like a vinyl window is, where a floor mat has all the ridges and valleys to get into,
3) Not sure if the yellowing is on the surface of the vinyl or within the thicker plastic that makes up the floor mat
Another "factor" that may cause this yellowing is the petroleum residue from asphalt roads and parking lots that gets on the soles of shoes. I know that asphalt sealers are notorious for this and are a major reason some light-colored carpets have a yellowish tinge to them in foot wells where the shoes end up (by the dead pedal on the left and under the accelerator pedal on the right), especially for car owners who`s workplace has had this sealer applied in late spring in their parking lot and they walk on it 5 days in-and-out during work week throughout the hot summer. I find it to be a "permanent stain" in floor mat and foot-well carpet fibers that is impossible to remove completely. I can get the worst of it out using WD-40 "Spot Shot", followed by Optimum Carpet Cleaner diluted 3:1, but not all of it.