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I disagree. This system can only be applied to 2D square games.

3D, 4D and hexagonal games shouldn't be classified like this. For
example, Raumschach has 125 squares (cubes,) which, according to your
system, is large. But in fact it's a very small board. Joe Joyce's 4D
Hyperchess has 256 squares (cells, tessaracts,) but it's really small.
[Consider that the restricted king of Hyperchess can go from one corner to
the other in 6 moves. A full 4D king which moves orthogonally, diagonally,
triagonally, and tetragonally can go the same distance in 3 moves.]

And of course, you're the Hex Chess expert on the site, you wouldn't
call the 91 cells of Glinski's Chess 'large'.

I think the size of the board is better classified in relation to the
speed of the king. If the king can cross from corner to corner in, say, 3
moves, it's a small board. And so on.