I'll note it's not just mental models, 'cause like. We have artifact siege weapons and ranged damage charms and the spears of war gods, all of which can be reliably assumed to be grander and more deadly than Some Dude With A Gun. Your guy with a rifle isn't outdamaging Glorious Solar Bolt or Elemental Bolt Attack, much less a Lightning Ballistae. Being very generous, we could give machine guns artifact traits but I don't really see a compelling reason to assume an M60 is better or even nearly as good to bring to a fight than Mahicara's lava fists or Fakharu's breath attack.Fundamentally the answer is going to revolve around 'is a machine gun noticeably more powerful than a dragon sigh wand without evocations' and if your mental model is yes then, sure, the Realm will have issues. If it's a no (which is equally fair), then the Realm is entirely capable of fighting an enemy with massed artifact ranged weapons but no good defensive traits, especially considering that the USA is relatively less mobilised and capable of tolerating losses than the Realm, which dampens the effect of all those artifact-grade weapons.
You can just give it heavy mundane weapon stats and some unique tags to make it better against battle groups and bam, you have a machine gun. Anyone with really good parry has a pretty solid chance of handling it, though, because weapons aren't special, the people who wield them are. Unless a legendary hero is manning it, you're not gonna be doing well against monsters that need legendary heroes to fight them.