That's always puzzled me, too. How do you commit treason against a state you weren't born in and had never lived in? As if the murder charges weren't enough to send him to the gallows, they had to toss in bogus 'treason against the Commonwealth' charges. That would be like charging every German, Japanese, and Italian POW during WW2 with treason and executing them.
As I recall William Joyce (AKA "Lord Haw Haw") was tried and hanged as a traitor by the British even though he was technically an American citizen.
I believe that he was also convicted on five counts of murder.