As for most of those examples I am showing an evolution of fighting forces, and trying to give a diverse perspective to show what could have developed from different cultures. Also giving the OP different reference points to look at for his idea about the infantry. Also Han Dynasty warriors could operate in 20 man groups very easily and for the technology and fighting styles of the day that is beyond impressive.
Like I said I concede the point about the exact term "fireteam." Marine's always came up with every tactical idea ever I get it, I really do, you can keep the term "fireteam." The idea of splitting squads into smaller groups to allow for covering fire, advancement, and split leadership is not a new idea; once again I know it wasn't called a "fireteam."
As to the topic of the post one of the big reasons for splitting a squad is to allow half the squad to advance while the other half is laying fire, and this tactic can apply to the biggest nastiest infantry advance you can think of. BUT 3-5 people seems to be the lowest number that the tactic works for. @ Charon I did my time in service and had to sit through hours of lectures and sweat through endless hours of drills, maybe I got a different instructor but he made sure to show us examples of what worked historically, what didn't, and why.
As for the Russians, I'm sure those 8 man squads never broke in half to attack from 2 flanks, wait yes they did. You are correct though they weren't called "fireteams." And you know what I bet in a GoI style infantry group they wouldn't have an exact Fire team structured A, B, C. But that's how it would naturally sort itself. The only thing missing from a natural fireteam compared to a marine fireteam is a SAW. The squad leader wouldn't put an idiot in charge of half his sqaud he would put the guy he trusts to lead the squad if anything happens to him in charge.
As for geeking out, you're getting so into the minutiae of the topic and not understanding the over arcing concept as it applies to the topic at hand. Deductive reasoning not rigid it must conform to this to be this. I know that's not how infantry is programmed but hey we aren't talking about American Marines in this forum.
The infantry in this world has been fighting for decades with firearms. They would have figured out effective means to fight. Maybe they don't have a special weapon like a SAW to form around, maybe they do. Would it really change infantry organization to the point where a 7-12 man squad is the smallest possible formation just because the don't have a SAW? NO. Blocking out, as I said before, the complete idiocy of straight line combat. Decades of war would have cured them of straight line combat.
Maybe they wouldn't have developed a special designation such as "fireteams" but the splitting of a squad naturally happens to maximize its effectiveness.