Left handed representation doesn’t matter in most games since the game controller in the player’s hand causes actions, regardless of the player or character’s handedness. But there is one exception, and many players – even right handed people – took notice when it happened.
Link, the most famous left handed character in gaming was changed to right handed for Zelda: Breath of the Wild on the Nintendo Wii. This was done for an obvious reason: the Wii controller is designed only for use with the right hand, and players’ actions wouldn’t match the action on screen.
But that begs the question: Why didn’t Nintendo program the Wii (not just for Zelda, but all games) with a left handed option so that left handed players could play? And people say “right handed privilege doesn’t exist!”
A 2015 article on lists five left handed characters in different video games.
Kain Highwind (Final Fantasy IV)
Freya Crescent (Final Fantasy IX)
Luke fon Fabre (Tales of the Abyss)
Mega Man (fires primarily left handed in the series)
Link (Legend of Zelda series)
One character not entioned in the item is “Doomguy” from DOOM and DOOM 2 (1993, 1994). Doomguy punches and uses the pistol left handed. He uses other weapons right handed, but this is more likely a reflection of reality. Few weapons are designed to be used right handed. I’ve seen chainsaws up close, and all are designed to be used right handed.
I plan to write a third item later when I get home.