Earlier quoted context omitted.
Good observation. Considering stacking of pieces maybe 1.5D though.
Chess has different pieces, which has higher entropy than a true 1d backgammon or 1d checkers with only one piece a field. You could play with pieces that have a value of 1..N instead. Starting with 2,3, and 5 value pieces, and splitting them as needed. Making it one-dimensional again, while keeping 100% of the rules. Final verdict, therefore: backgammon is 1D, not 1.5. We could pretend that the second dimension was…
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.