Wikipedia has more.

[The Armed Forces Enlistment Contract states]: "In the event of war, my enlistment in the Armed Forces continues until six (6) months after the war ends, unless the enlistment is ended sooner by the President of the United States."

But, yeah, it's deceptive at best.

Back during World War 1, the Supreme Court ruled that the Thirteenth Amendment doesn't apply to the military. In the context of ruling about the constitutionality of the draft, they devoted one paragraph to the Thirteenth Amendment issue:

As we are unable to conceive upon what theory the exaction by government from the citizen of the performance of his supreme and noble duty of contributing to the defense of the rights and honor of the nation, as the result of a war declared by the great representative body of the people, can be said to be the imposition of involuntary servitude in violation of the prohibitions of the Thirteenth Amendment, we are constrained to the conclusion that the contention to that effect is refuted by its mere statement.

In other words, they said that they don't want it to apply, so it doesn't.