Mechanical engineer Brian Ignaut is the guy who designed SpaceX's unfolding solar arrays, then branched out into designing and building origami-like unfolding furniture under his own company, Degrees of Freedom. While prototyping a new design for an expanding table, he discovered a new way to make multiple surfaces fold relative to one another, which he then adapted into a chessboard:
Ignaut's brief development story is below:
"In the design, four wood panels are connected by six stainless steel links, four of which are used in pairs while the last two are used alone.
"The link pairs keep the joined panels parallel during all movement, while the single links permit rotation between boards which is used when pivoting the board into its playing orientation.
"I originally tried using this mechanism for an expanding table concept, and only came across the secondary crossing functionality after I started playing with the first prototype. I've been dreaming about this design for well over a year so it was fun to finally see it take shape!"