The firearms referred here aren't new designs, many of them are referred in the lore as being contemporary to the times of xcom, and are still being used because they're either leftovers from said period or the only things the general populace outside of the major factions are allowed to manufacture/use. I mean, RPGs, magnums, desert eagles, double barreled shotguns, etc, are all still around, so its does make sense for old guns to be around as well. Most of the common rifles are all old designs and not "firearms designed centuries into the future".
Hell, even the most advanced UAC weapons are centuries old, given how the UAC, in the xpiratez universe, seemingly existed at the same time as xcom and didn't last for much long after the aliens took over, being allowed to function until a disaster happened and brought the dark ones into the world.
One of the most flavorful things in xpiratez is how the gals, for the most part, aren't outright making new weapons based on alien tech, like xcom was, instead they're taking the weapons they can get their hands on and modifying them with new tech to make newer, better guns, or even just making newer, better ammo to use with them. Which is why I like the concept of specialized high tech ammo making older guns relevant again, like eletropulse and acid munitions, or stuff like the smartgun, which turns the AMG into a much better and accurate weapon.