It is broken for everyone. Comments on the video are filled with people complaining about the issue. It appears to be an issue with Youtube. A few youtubers have been having problems with their Youtube videos being stuck at 360p or not uploading properly recently.
If you go to the video settings in the bottom right hand corner before trying to play the video you should be able to set the video to 360p and then be able to play the video at that resolution.