Yeah you're right, it seems like the article is misleading. Still, unless I'm reading it wrong it seems like the patent is just describing the hardware translation of this algorithm, it's not really adding anything new. It's still dubious to me.
Yeah, isn't the translation to a circuit even more trivial than the algorithm itself? a / 2 and b / 2 just discard bits. a & b & 1 is just an and of the two low bits. Then we just route those values to an adder (with carry).