Just like people all animals are born with relative levels of innate aggression/submission around some (probably small in case of cats) standard deviation. So, yes, some kittens are going to be naturally more aggressive and some more passive within the population "cats". And just like people, nurture has a tremendous effect on the realization/elimination of aggressive tendencies. Abuse a cat for most of its life and it will probably react with fear/aggression towards every human it sees. Love it and it will likely never act on it's innate POTENTIAL for higher levels of aggression (assuming it has them) because there's not reason for them to actualize. So, yes. there is obviously variability within a defined range. All that being said - it's extremely difficult to say if the kitten was even showing aggression or if it was fear or if it was just playfulness and I'm not sure
A possibly useful story: ZahrasHuman and I had a first hand experience with a kitten that was SO intractable and SO overcome with separation anxiety that it literally made itself sick. (we now rather unceremoniously refer to this cat as "Bastardo"). We were prepared for the "demon under the bed" but this was a whole new level previously unwritten about. The darn thing literally growled at us (a momentary pause from the hissing) and refused to eat, drink, use the restroom or even come out of his carrier for over 3 days. In an effort to get him to eat we took the carrier away on the third day and he just shivered in the corner. Growing increasingly concerned, and after communicating with our breeder, we took him to two different vets - both of whom said while they were used to kittens hating the vet, this was the most aggressive kitten they had
ever seen. The second vet, who was our breeder's vet, actually demanded to the breeder it be returned citing it as the most difficult kitten of any breed he had ever seen and noting that it was clearly not ready to leave the nest and was headed down a very bad path health wise without a change. Note that our breeder had offered to take the kitten back before this had happened but we didn't want to abandon the poor little guy just because it was a rocky start - because that's not how family works. But when it became clear the separation was becoming a legitimate health threat we took the kitten back and got Zahra (who was our first pick anyways, but wasn't for sale at the time).
Now, Zahra, the female we got in exchange for Bastardo is hands down the most amazing and loving cat either of us have ever seen and it's not even close. Same breeder. Same litter. Same people. Same environment. So what happened? What happened was completely different innate personalities and temperaments. Now, were it not for the self induced high fever, eye infection, and starvation I am 100% confident we would have eventually worked through the issues with nurture. As it is, he perked right back up and immediately started eating as soon as he was returned. In fact, it may be that he was actually on the very low end of the aggression spectrum and very high on the attachment spectrum such that what appeared to be aggression was actually fear and attachment. In this way, you can see that temperament varies genetically but that environment makes a huge difference and "aggression" isn't always about aggression, but rather quite frequently the opposite.
Here is ZahrasHuman with Zahra: