The "dimensions" in these board games isn't a mathematical/topology thing, is it? Normally one dimension = one real number space. Every board game ever would fit in 1D then, "2D" chess included.
I'm fine calling Backgammon 1.5-D. Physically you focus on a single dimension, and the second one matters too but it's not the same.
I'm fine calling Backgammon 1.5-D. Physically you focus on a single dimension, and the second one matters too but it's not the same.