The takeaway from the linked article…

“The majority opinion, written by Justice Anthony Kennedy, found that the constitutionally guaranteed right of habeas corpus review applies to persons held in Guantanamo and to persons designated as enemy combatants on that territory. If Congress intends to suspend the right, the Court said that an adequate substitute must offer the prisoner a meaningful opportunity to demonstrate he is held pursuant to an erroneous application or interpretation of relevant law, and the reviewing decision-making must have some ability to correct errors, to assess the sufficiency of the government's evidence, and to consider relevant exculpating evidence. The court found that the petitioners had met their burden of establishing that the Detainee Treatment Act of 2005 failed to provide an adequate substitute for habeas corpus.“