Though I would build a chess board out of veneer and MDF - and have done so and taught others countless times -
@stratamania is right.
What bothers me a little: Usually in a solid guitar body, the direction of the grain is (about) the same as the strings, which seems quite logical, as the wood has the most mechanical stability and the least hygroscopic movement in that direction.
In a checkered body however, for the different pieces to be glued together properly, the end grain is facing
up, in the direction of the polepieces, if you will.
I saw a YouTube video once, where they build a guitar body using a similar method and it seemed like they sealed the whole thing with epoxy to avoid any issues.
I would be curious to learn more about how Warmoth did those.