So based on this;
The Predators began as the Hish-qu-Ten which means the term Yaujta came later. So Hish is
used to describe them, just in an earlier period of history, whether they called themselves this or if it's a name given by the invaders is unclear. The Amengi (presumed to be the species for the original Predator before the Winston redesign) had invaded the home-world and enslaved them for gladiatorial combat and labor. The Amengi however engineered their own defeat because through this process of breeding warriors hell bent on killing they eventually overthrew their masters.
With this information in mind we can surmise that the origins of the culture seems to stem from gladiatorial combat and guerilla tactics used to fight the Amengi. The box also says "thousands of years" which doesn't jive with what we know about ages of various Predators but this could also be viewed as thousands relative to the Alpha given that Alpha simply wouldn't have survived into the modern day. I say this since we know the earliest point in the timeline at least on Earth is the dawn of Humanity which the Predators played a small role in.The Amengi are not seen in the flashback in AVP so we can safely assume this would take place after they overthrew them.
Interestingly while it seems to imply an origin for how they use their gear it doesn't say the Amengi gave it to them. Infact if this is taken at face value it means that early Predator weaponry is fashioned from ripping apart one of their masters and converting it into weapons and armor.