Upvote:3
I think you're looking for Edward Hyde, later the 3rd Earl of Clarendon, who was the British governor of the colonies of New York and New Jersey, 1701-1708, decades before the USA because independent. He's famous for cross-dressing, among fans of ludicrous history.
However, the US office of governor seems to descend fairly directly from that of the British colonial governors, so he's probably the man who that video is talking about (I gave up after a few seconds, it's too hard on my eyes).