No. It's clearly a federal reservation - federal property. It's complicated and there are some limited circumstances where a murder on a base could be prosecuted under state law, but this case isn't one of those cases. The military will get first crack, then the feds if Obama - and it would be Obama's decision, decides to move it to federal court.
I would very surprised if he wasn't prosecuted under the UCMJ. What will be interesting will come at the conclusion of the trial and after the exhaustion of appeals - which will take 12-36 months. Unlike a civilian federal case where the death penalty is sought, in a military dp case, the CIC will actually sign the condemned death warrant. IOW, Obama will have to physically sign a document ordering his execution. That should make for a challenging political decision for Obama.
Obama will pass that one on. He will find some to delay that decision.
I agree that under military law, the military via Courts Martial has first crack at this POS and can impose the death penalty. But under Federal law, unless he killed a protected Federal official (CIA, FBI, Elected Official etc.) their are no Federal capital offenses involved. Keep in mind that McVeigh was not executed for killing a couple hundred civilians in the State of Oklahoma. He was tried and convicted in Federal Court for killing a handful of protected Federal law enforcement agents.
With my meager knowledge of the law, killing a GI, or a civilian on Federal property, is not a capital offense under Federal law. But murdering anyone, anywhere, in the State of Texas, on Federal property or not, can be a capital offense.
This POS is subject to the USCMJ only because he was a member of the US Military. If he had been a civilian walking on to that base, it would only be the State Courts to impose murder charges.