Just makes me think there's a market for a better brickie robot. The one they show is lethargic and built like a train. Even two robotic arms, working like a human does would be tons more efficient. (I'd also like to complain about the stupid title, but it's what NYT picked)
I'm thinking something like a robot with treads, that can move in a straight line (or maybe curves), perhaps at the end of a long boom with a conveyor on it that moves bricks from a central source.
It basically grabs a brick off the end, squirts some mortar down, and lays the brick. Make the bricks shaped in a special way so they interlock better and need less mortar at the edges (they already have bricks something like this; they almost look like lego). Then it rolls to the next brick position.
Once it gets to a certain point, it "crawls up" to the next level, perhaps by gripping the level below with the treads (the mortar will probably need to be some kind of "ultra-fast setting" stuff; possibly more like epoxy than mortar), and lays the next layer, being guided by the last.
I guess I'm just saying this particular brick laying robot looks like it was designed by an engineer who, back at the beginning of heavier-than-air flight, thought an airplane needed to flap its wings to get off the ground...