in grid.drawGrid(), where it's drawing the grid:

beginShape (); vertex (x4, y4, z4); vertex (x1, y1, z1); vertex (x2, y2, z2); endShape ();

you need to define the texture to use and modify the vertex calls to the version that also adds texture coordinates - vertex( x, y, z, u, v) . (you'll also need to specify the other point as he's only drawing two lines and you need a quad). there's an example in the examples (Texture Cube).

this will obviously have an impact on performance