"Get out" does mean "go away" or "leave"; however, that's not it's only meaning. It also means "pull out" or "bring out". In this case, Anger is asking them to "remove the rubber ball from wherever it might be being kept" so that they can presumably play with it. Apparently, there are more than one person in solitary confinement with him, which is strange because solitary confinement should mean that he is alone. Anyway, it just means to bring something out of where it's being kept:
"Get out your baseball bats and gloves; we're going to play baseball
in a few minutes."
The "out" can also be postpositive here:
"Get your baseball bats and gloves out; we're going to play
baseball in a few minutes."