Keys are mapped to specific locations on the typeball. When you rearrange the letters on the typeball you remap the mapping between keys and the actual letters that get printed. So you get a different effective keyboard layout.
The idea would be that you would replace the "A" on the ball with the character that is in the QWERTY's A position the Dvorak keyboard, etc.
Exactly! A was an ironic choice for an example, however, because it's the one character in QWERTY that's got identical placement on Dvorak.
Nit: 'm' matches as well. I think it's those two only.