There's something that bugs me about this game. It takes place in a more fantastic version of the world during the 19th century. The lead character uses swords like cutlasses, short swords, longswords, and broadswords. The sword actually did survive well into the 19th century... but swords like that would have really only have seen ceremonial or military use. A wealthy British aristocrat like the lead character would have used a smallsword like a rapier for sport or self-defense.
Keep in mind that this version of the 19th century has a vast abundance of Adventurer Archaeologists, and that the whole reason the Brown family is aristocracy is from his mother's side, not his father's. It's entirely plausible that Gilbert trained Edward in more unconventional swords in between his exploits.
There's also the key part of your statement: a more fantastic version. In an early scene we see Gilbert swat bullets from multiple machine guns away with a borrowed sword. And Edward can hack Eldritch Abominations to pieces with whatever he happens to be holding. Basically, swords are practical weapons in a world where Charles Atlas Superpower and Super Natural Martial Arts exist.