Though there is common law contempt, in the US it has been codified in statutory law[1]. The text of the law states that it is indeed a punishment for disobedience with the court.
In general, "revenge" is not the aim of any administration of justice; however, punishment is a tool, for better or worse, that is used in an attempt to achieve justice. Punishment is also the type of remedy that the state can do well. The maxim about "have hammer; see problem nails" applies to the state as well.
Keep in mind that the statute, enacted by Congress, explicitly allows the exact punishment Manning herself received. While holding her beyond the grand jury proceedings was considered moot, the fines themselves survived, as fines are wont to do.
You're right, there is such a thing as criminal contempt, which can be used punitively. But it is a crime for which you have to be charged and convicted. Chelsea Manning's contempt is the civil variety, which must have a coercive purpose.
