He's literally the leader of the armed forces, he has all the power he needs to shut that place down any time he wants.
Point is that shutting down Gitmo was something the Administration attempted to do and that Congress forcefully blocked.
"The President...shall have Power to grant Reprieves and Pardons for Offences against the United States, except in Cases of Impeachment."
Article II, Section 2, Clause 1
They are detainees of the USA. He has full power to bestow each and every one of them a full unequivocal presidential pardon for all crimes accused and committed against the US. No if's, and's, or but's.
If you aren't willing to gamble that you'll need/get a Presidential pardon, then you clearly don't know enough to justify what you're about to do to the suspect.
That'd be a little less extreme, and a little more, I dunno, constitutional?
Actually, the Congress governs the armed forces; the Constitutional designation of the President as Commander-in-Chief simply means limits the Congress, in adopting rules governing the military, from appointing someone else as supreme commander of the military within those rules.
The President isn't the King of the military, or anything else.
Gitmo does not get closed by one lone person..it takes Congress