From an RF standpoint, this video is completely incorrect. It will reduce your range and cause problems. Wrapping it like that is definitely wrong.
The thinner section at the end of the "antenna" (actually a tiny coax) is your antenna. This last section should be straight and preferably vertical or horizontal. An antenna with a shorter coax and/or creative routing (gentlest curves possible) will allow you to keep it entirely within the body. Changing the antenna/coax attached to your radio to a shorter one (search LXBGCP at Tower Hobbies for an example) will make it easier/cleaner.