lol, what a joke of a video. Jupiter most certainly does orbit the Sun, what the hell else is it circling due to gravitational pull? (besides the the super massive blackhole at the center of the Milky Way)
Also to note, all gravitational objects pull on each other, but lets be clear. The video shows Jupiter pulling MASSIVELY against the Sun. That isn't even remotely close. Yes, Jupiter wobbles the Sun, but understand. The Sun contains 99.996% of all the mass in our solar system. That means Jupiter at tops is half of 1 percent of the weight of the Sun. If you weight 200lbs, Jupiter would at tops weight 1lb compared to you. Is it enough for you to feel the pull? Yes. Is it going to throw you completely off balance as depicted in the video. No.
btw, two stars of the exact same mass can (and do!) orbit each other. (read the definition of the word orbit!) Pretty much all orbits are elliptical and not perfectly round.
This is orbiting.
So is this:
and so is this