"Power Struggle When revealed, the opponent to your left chooses 1 Lord and 1 Lady character,if able. Then, you must choose and kill 1 of those characters. The other claims 2 power."

Just to make sure: If the character chosen for being killed is saved the other character still claims 2 power. Right?

Sure.

If it was worded "Then, the other claims 2 power", the power claiming would be dependent on successfully killing the first character. The way it is, saving the first character doesn't impede the power claiming.