(Sighs) Can't believe I'm doing another one.
What's the Work
I'm just gonna copy-paste from my Darth Nox removal.
Star Wars: The Old Republic is an MMORPG set thousands of years before the events of the films. You're given the option of joining the Galactic Republic or the Sith Empire, with the story playing out based on your actions in-game.
Who is the Emperor's Wrath
The Emperor's Wrath/The Empire's Wrath/The Sith Warrior/The Acolyte is one of the playable characters for the dark side of the Force. They start out as the apprentice of Darth Baras. He places them under multiple tasks and tests in favor of Overseer Tremel who plotted to use the Wrath for destroying Vemrin. They eventually discover this and kill Tremel. In Naga Sadow's tomb to retrieve an ancient lightsaber, they are confronted by Vemrin, but defeat him. His daughter Eskella attempts to avenge him but the Wrath kills her too.
Becoming the full apprentice to Baras, he orders the Wrath to complete multiple missions in assistance to stop the Republic from stopping their advancement from defeating the Empire, but also including assassinating multiple people Baras claimed to be traitors, such as the slaves of Darth Vowrawn who threatened to expose Baras' involvement in supporting a rebellion to tarnish Vowrawn's reputation. Eventually, Baras betrays the Wrath once they outlive their usefulness to him, angering the Wrath to battle against Baras. After they defeat him, the Wrath is given the option to execute Baras in front of the Dark Council or instead exile him to an asteroid at the edge of the galaxy. The Wrath is then promoted to becoming right-hand of Emperor Valkorion. Now known as the Emperor's Wrath, they are given the option of serving Valkorion, or possibly killing him to become the Emperor/Empress themselves.
Why they don't qualify
Exactly just like the case with my removal for Darth Nox, the entire game is completely player-dependent. True that the Wrath is given more sinister and sadistic options to choose from; such as killing Lord Grathan's wife just for witnessing them kill her son, eliminating both Baras and Draagh the instant they betray them, and killing multiple people connected to Jaesa Willsaam to break her innocence and fall to the dark side.
But at the same time, the game does give you playing as the Wrath the option to choose a "Light-side", where you can go Noble Demon and respect your enemies, even the ones the game forces you to kill to advance the plot. It's even possible for you to develop romantic relationships with your companions, even if you choose to play aggressively.