I am also more curious about the 9-dimensional Space shogi, https://en.wikipedia.org/wiki/Space_shogi ... "Black starts the game occupying levels 1 through 3; White starts on levels 9 through 7."
Isn't it just 3-dimensional (9x9x9)? That's a smaller playing space than taikyoku shogi, it's again a game equivalent to chess (in the von Neumann sense) and a computer wouldn't find anything more conceptually difficult about moving through a 3d array than a 2d one. So I'd expect the computer's advantage to be even larger here.