I started by setting up the playing with some simple embedded for loops, that'd alternate between white tiles and black tiles. Each of the tiles has a position in the form of a 6D Vector and a Reference to a piece, if one finds it itself in it. The Controller for the Cursor was rather easy with Unitys Axis Input manager. I then created a Piece class, that'd save all the directions the Piece was allowed to move in an array of normalised 6D Vectors. Once a Piece is selected, it'll loop through each of the Vectors through the value i and will check the tile at direction*i. if there is no obstruction, it'll be selected by setting a flag in the tile class and changing the color. If there is a piece in the way however the direction will be added to another array called blockedDirections and every time it loops through it it checks that !blockedDirection.contains(direction).
The Code behind Interdimensional Chess