The principle of habeas corpus (lit. have the body) is generally concerned with the right of a prisoner to appear before a court.
I cannot see how any law that intends to apply a suspension of habeas corpus only to “Enemy Combatants” can get around US Const. Amendment 14, § 1:
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside. No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
Note that the emphasised section says “person”, not “citizen.”
Perhaps there are judicial precedents ruling that secretly the amenders only meant “people we like.”