Yep, that's the old style arm and the ball is not removable from the arm.......it's all one piece. The ball is now damaged, so, you've got to remove and replace the arm........and it's probably been in there for 40 years. Not a terrific task.

You probably have iron pipes coming up the wall to the shower head. If so, they can take the torque that you're going to have to use to get that arm loose. You'll definitely need pipe wrench, and, hopefully, you won't break the fitting in the wall. But, at that age, nothing is certain. Can you remove the one tile around the arm and get to the fitting? A good bit of heat from a propane torch will make short work of getting it out without damage.