Is there any requirement that mandates a residential floor-installed electrical receptacle to be a GFCI type, when said location is in a dining area, NOT located in the bathroom, kitchen, laundry / NOT near water source? Thank you!
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.