Floor-Based Electrical outlet type
No, this receptacle doesn't have to be GFCI protected

The primary clause that requires GFCI protection in residential kitchens only applies to kitchen countertop receptacles (there's also a GFCI requirement for dishwashers, but that's a different thing):


  (6) Kitchens — where the receptacles are installed to serve
  the countertop surfaces


However, it does need to be installed correctly

The problem with a receptacle in the floor, though, is that putting a regular box and receptacle in the floor yields a hazardous installation (due to crud getting into the receptacle), and is prohibited by 314.27(B), which requires a listed floor box and matching faceplate be used instead:


  (B) Floor Boxes. Boxes listed specifically for this application
  shall be used for receptacles located in the floor.


So, you need to make sure the box is listed and labeled as a floor box -- these will generally have a distinctive faceplate that has flip-open covers over the receptacles themselves.