No, it sounds like a run-of-the-mill breach of contract lawsuit.

As alleged, Snowden signed a contract where he agreed to do certain things, X, for the right to do Y. He did Y but then didn't do X. And now the counterparty is suing for damages under the contract.

The US government has limited power to stop publication, so all Snowden had to due was submit the manuscript for review, reject any requested changes, and then go ahead and publish the book in its original form.