it means "they have not anything to do"
it is bad very bad grammar. It should not be used, other than in you knowing that "they have nothing to do"
"they have not GOT anything to do" <-- should never be used.
Also, the two parts of the quotation do not match, they appear to be contradicting each other.
O.K—O.K. I’ll tell ya again. You think I ain’t got nothing to do. Might jus’ as well spen’ all my time tellin’ you things and then you forget ‘em, and I tell you again.
I do not know where you haeard this nor do I know the full conntext, but I think I may have added the missing part that connects the two and makes it flow better.