So here's the pistol from Predator 2.
There the hero gets it from the Predators who reveal themselves in the end after he kills the Predator he fought with. They do it in acknowledgement of his deed, to the honorable opponent who triumphed in a fair fight. It's a trophy. It has to be a revered trophy to give that, and not another weapon they took anytime, maybe around Arnie's adventure, since then or earlier. And the viewer assumes it's from someone who was very hard to defeat, someone who had to kill one of them, they had to pay a high price for it. Perhaps that Predator who died on that occasion was killed with the pistol itself. Since there is a date on it, while the pistol could have been used any other time (yesterday too), it has to signify the date when those events happened - although the date itself doesn't mean much in the context of this post.
But in Prey, the girl got it from a French bloke (who was the least asshole), and gave it to her tribe. While she shot at the Predator with it, it had little role in the fight. Now how this weapon gets into the Predators' possession? They clearly put it into the movie to establish continuity, and make the events in Prey canon, so it is an important piece. Are they gonna make another movie featuring the pistol a bit later after the events in Prey?

There was some other thing I wanted to write about, but I forgot. Oh well.