Lago is a charismatic character, yet he is also deeply manipulative. He uses his understanding of other people to root out their weakness and turn it against them. This means that the people he hurts are not only his victims, but victims of their own flaws. This is not unusual for a tragedy, as one of the most common ways for a character to meet their doom is from themselves, figuratively or literally.
Using the characters as metaphorical chess pieces is a smart move on Lago’s part, as it means that the characters will further his plans on his own without his direction, so he doesn’t have to waste time on them. It also makes his plots harder to see for the other characters. If Lago stays in the background, then the other characters have less of a reason to find him suspicious. Lago is a Mastermind type of villain; in that he is intelligent and uses that to his advantage.