This design would probably work just as well with a square tube acting as the base for the second segment of the arm, it's just another way of getting the job done. Even so, I like the round tubes because you can clamp arm components together with t-bolt clamps. It seems like a stronger and easier to maintain system to me.
I really prefer using a round tube for the mast, though. In 2007 our mast was made of a 3" diameter, 1/16" thick 6061 T6 aluminum tube. This thing was plenty strong for a FIRST robot, and it only weighed 0.70 lbs per foot. Since most square profile tubes of similar size don't come thinner than .125", they will weigh at least twice as much. (you could cut speed holes in a square tube, but that takes too much time and effort for us
)