I searched a little but didn't see mention of this guy's single tree setup. He has lots of other entertaining videos on his channel as well.
I tried it in the backyard and it works great!
I secured one end of the hammock to a tree using a strap and whoopie. A 6-foot scrap piece of 2"x2" served as a pole, which I connected to the hammock and a short fence post with mule tape--thanks JohnSawyer! I used a pair of Siberian/Evenk hitches that Peter uses in the video to keep the pole in place, and a trucker's hitch to secure the pole to the fence post.
I was hanging just a few inches off of the ground (just in case!) but after a couple hours of hanging, many times in and out of the hammock, and some vigorous swinging I have plenty of confidence in the setup. Even the dog approved and hopped in with me.
EDIT: The hammock in the video is very taut, but I was able to get a great hang with a gathered end hammock.