Hence the video what? It's polar coordinates making the spiral, not prime numbers.

The primes >3 are all of the form 6k+1 or 6k-1, so they are close to 6k. As k increases, the resulting marks on the polar coordinate system form nearly complete turns because 6 is close to 2 pi. Hence, spirals. See my other comment for a clearer explanation of why primes >3 all must necessarily be one more or one less than a factor of 6k where k is an integer. That is the crucial piece that the author did not make totally clear.

So what does it look like if you fudge it by scaling 2 pi down to 6 ?

A straight line of pillars.

This is pointed out in the video

Hence the video making it extremely clear pretty much right off the bat that yes, any integer plotted that way will form a spiral. The video then goes into a very interesting discussion IMO into why you see the specific patterns of spirals and rays with the primes.