That does. Each character would have to have their own fighting style and/or weapon, though, fitting with their stories.
For example, in the Grimm version of Red Riding Hood has her cutting open the wolf and setting her grandmother free from its belly, so one of her weapons might be a small yet very sharp and quick knife. She could use her cloak to flutter into her opponent's face while she spun, blinding them a moment so she could jump away or pull off an attack to a critical area like a disemboweling (Red's version of a fatality).
Jack, I believe, is or was the son of a woodsman or lumberjack in the original story, so his weapon would be something like a giant-sized knife, lumber axe, or over-sized saw-blade sword. Being able to kill giants, Jack would also be the strongest of the fighters, able to deal the most damage and gives a great deal more knockback-effect on opponents. This would make blocking Jack's attacks a bad idea as the opponent would still be damaged and be pushed back; maybe not much, but more than blocking against others. Maybe even give Jack a type of shield-breaker ability. An idea for his special ability would be to plant beans in parts of the arena to create climbable areas or ride the stalk up as it grows then jump off and impale his opponent or simply split them in two.
I haven't read the story with Corvetto, but checking the wiki attached to his name, he sounds more like a rogue, which would still fit in a gothic brawler. He'd have the ability to hide in the fighting arena, setting up traps or moving to other parts of the arena unseen to come up behind his opponent. His special ability would be being able to use the environment more than anyone else. And with this place as a servant of royalty, he'd have a very refined fighting style, like fencing, making his best weapons be a rapier.
I'd love to play the game if you decide to make it. I'm not very good at fighting games, but if you ever need ideas for the characters, let me know. I'm more than happy to help.