I think it's 5D because it just skips the "our" 3rd dimension. Just because Chess movements are in a 2D space, doesn't make the 3rd dimension temporal. You can move in 2 spatial dimensions and 1 temporal one (the 4th), but when you move through the temporal one you create a split in the 4th one...
"5 - a split" https://www.youtube.com/watch?v=0ca4miMMaCE
Of course I'm assuming you're all playing the game in the same universe I am!
In other words - the game USES 4 dimensions, but is PLAYED in 5D.