Your definitions of "war" and "military" are outdated and unrealistic. The war against al Qaeda and the Taliban is a proper war, being conducted by our armed forces.

The combatants rightly fall under the category of "unlawful combatants" for purposes of the Geneva Conventions. This means that, generally, they may be tried by military tribunals and sentenced unless they are on US soil when captured, though it may be that some such individuals could be tried in military tribunals nonetheless (if there were evidence they acted as spies or saboteurs, for example).

The only issue, from a Constitutional standpoint, is whether or not they had rights which were violated. The Supreme Court ruled, in Boumediene v. Bush, that they had a right to make habeas corpus petitions. This does not translate into an automatic right to a trial in Federal Court, however. It merely states that the 2006 law, as written, did not extend those rights or make a valid suspension under current law.

The proper venue is a military tribunal and the proper outcome is summary execution. None of this violates the Constitution.