How has the empire not just obliterated the rest of the world?

[LineageRazor]

To specifically address the "guns vs swords" angle, the reason why guns are so "ineffective" is related to the reason why a three-foot Lalafell can swing a sword and deal as much damage as a burly seven-foot Roegadyn. EVERYONE who isn't a Garlean uses magic bascially all the time. It's so deeply ingrained in them that they don't even think about it. This makes them stronger, faster, and more durable - and since Roegadyn possess about the same amount of magic as Lalafell do, they wind up being equal in strength. When talking weapons, a sword wielded by a magic-wielder hits just as hard as a bullet fired from a gun - and when it strikes another magic-wielder, a gun only does as much damage as a sword would.

Garleans, historically, were at an ENORMOUS disadvantage because of this. The magic-wielding tribes easily pushed them out of their original territories into the inhospitiable Ilsabard areas, where they made a meagre living until Emperor Solus rallied them and made use of uncovered Allagan technology to provide tools that evened the playing field. That's right: evened. Those guns and bombs could only do that much, thanks to the magical resiliancy of the magic-wielding people. Fortunately for the Garleans, their first few conquests granted them additional armies of conscripts, forced into battle with their families essentially held hostage, and each nation taken snowballed the Garleans' power to the point where they were essentially an unstoppable juggernaut.

Then, they encountered Midgardsormr, their first crushing defeat against a completely unexpected and unknown enemy, which stalled and confused them to the point where the Eorzeans were able to claim other victories, as well. They probably COULD have rallied and continued the conquest unabated, but it's likely that Emperor Solus saw a good opportunity to rein his Empire in. Nael wanted to call down Dalamud, and Solus knew very well that Bahamut was trapped inside (heck, he was there pulling the strings from the shadows when Bahamut was trapped in the first place!), and so was all for the plan. It was a perfect opportunity for a Calamity, and it worked like a charm (even if the full devastation was tempered by Lousioix's sacrifice). Bahamut was freed, Calamity happened, another Shard was joined to the Source.

By the time all was said and done, Solus's human body was on his deathbed, and after he passed no one was able to lead the nation as compently as he had - and he'd organized things to make certain this would be the case, much to his successor's frustration. Solus wanted the Empire to be strong and dangerous, but he could only allow it to be overwhelming for so long. There had to come a point where others were able to stand against it, to enable the conflicts necessary to trigger yet another Calamity.