The reason it's showing those interesting paths is because it's plotting the relative motion of the planets with respect to the Earth.

So visualize the moving Earth in the center of each image with the other respective planet moving relative to the Earth. Since both are moving and rotating about the Sun we get these interesting motions with a lot of structure.

This is the theory of epicycles which was the main theory of the motion of the planets before the heliocentric view became prominent.

And if you like those, check out the orbit of Cruithne:

https://www.youtube.com/watch?v=BmbuSR-fOZM

https://en.wikipedia.org/wiki/3753_Cruithne

Cruithne orbits the sun at about the same distance as the Earth, and so with about the same period as the Earth. The orbit varies, so sometimes it's closer to the sun than we are, and sometimes further from it. So, seen from the Earth, what it's doing is moving around us - sometimes ahead of us in orbit, sometimes sunward, sometimes behind us, sometimes starward. But its orbit isn't pefectly elliptical, and it has more inclination, so it traces out an interesting path.

That video is a recycling of an older video which had a very informative voice-over, rather than some cheesy music. That video doesn't seem to be online any more, sadly.

Cruithne's orbit was only figured out in 1997, and i remember that it was briefly very cool (for small values of cool). Stephen Baxter, who was a top science fiction writer at the time, featured it in his novel 'Time'.

Steven Fry in an episode of his funny informative show QI incorrectly called Cruithne Earth's second moon. It's not; it orbits the sun, not the Earth. I don't think it's ever directly sunward or starward from us, but always either in front of us, behind us, or on the other side of the sun.

From the article: "From left to right, these rosettes show the surprisingly beautiful paths of Mercury, Venus, Mars, Jupiter, Saturn, and Uranus as seen from Earth. "

https://earthsky.org/space/what-is-retrograde-motion kind of gives you an idea

When on earth, everything looks like a moon.

Learnt something interesting today. Thanks for the cool link!

Before we understood that the planets orbit the sun (more or less), astronomers thought they orbited the earth, and tried to explain these paths using epicycles - note the diagram halfway down:

https://en.wikipedia.org/wiki/Deferent_and_epicycle

... which always make me think of my limited understanding of string theory. :-)

(Which can be summed up into "something something resonance something something dimensions".)