The only difference between 2d paper miniatures and metal flats is the material used. People use buildings made of paper, wood, plastic, resin, and metal. Figures vehicles and ships are also available in plastic and resin along with paper and metal.
Early miniature wargaming was often done with flats (two dimensional metal figures) instead of rounds (as three dimensional metal figures were called back then). Tony Bath, who ran the famous Hyborean Campaign and was a founder of The Society of Ancients, gamed with metal flats. Two dimensional paper soldiers have existed for decades. People game with two dimensional paper ships. The two dimensional paper soldiers, etc are not full size, therefore they are miniatures of the real thing.
People use the plastic figures from board games for miniature wargaming without painting them. Where is the modeling in that? There is nothing in the definition of miniature wargaming that says anything about modeling being required. If you buy an army at an estate sale or a used army from a friend or on ebay and do nothing with it other than gaming are you then not miniature wargaming?
I have seen wargaming tables with terrain represented by paper or cloth roads, waterways, and fields. Hills, woods, and other terrain features have been represented by cut pieces of cloth. Just look at what is often used in tournaments. Those are not models of the actual terrain, but it is still miniature wargaming.
Definition of miniature from dictionary.com
a representation or image of something on a small or reduced scale.
a greatly reduced or abridged form or copy.
a very small painting, especially a portrait, on ivory, vellum, or the like.
and this from the Oxford dictionary
Represent on a smaller scale.
‘she saw her own reflection miniatured'
and here is the definition of model from the Oxford Dictionary
A three-dimensional representation of a person or thing or of a proposed structure, typically on a smaller scale than the original.
We are not "model wargaming". We are miniature wargaming.
As a final note, all my miniature soldiers, vehicles, etc. are three dimensional items. That is just what I prefer to use.