I didn't know he played. But..he is fingering a G-shaped chord at the IVth fret, which would basically make it an Aflat Maj 7th, especially if he played the open strings also, and the open D string would give it a Lydian sound.  And...probably unbeknownst to him a Major 7th works very well with Lydian...might have a very lush (lush...get it?...oh stop, stop, you're killing me with that) sound.  I gotta try it when I get home.  

Hey, Ma looky heah.....the Prez is playing an Amaj 7th Lydian chord on the geetar...sheeit, I didn't know he could do that!!  I'm gonna vote fer him again!