I've seen lots of theories on Gael, what happened to him, and what the dark soul is. I don't have all the answers, but I think I can clear some things up.
Gael wanted to get the dark soul. "But all humans have dark souls. Whhhyyyy?!?".
I DON'T KNOW OKAY I'm glad you asked. Gwyn and the four original lords had their souls, but Gwyn snapped little bits of it off and gave it to some guys. When you speak to the friendly pilgrim lady at the start of the dlc, and ask her about the Ringed City, she will mention that the Lords walled off the Ringed City, and the dark soul is there, better left alone.
Why, where did you hear that name, love? Oh, it doesn't matter. I'll tell you what I know. The Ringed City is said to be at world's end. Past this heap of rubbish, as far as one can go. But you'd better think twice. The forsaken Ringed City was walled off by the gods to contain the pygmies. …and the dark soul is better left well alone
So we know that the Dark Soul is still a separate soul. The first furtive pygmy found the first dark soul, which was spread to other proto-humans. But it looks like maybe the original dark soul still existed. Their are multiple dark lord pygmy guys, so maybe the dark soul was split to multiple successors of the first pygmy?
"Okay, but why does he say he wants our dark soul?"
Keep in mind this is all speculation, but here is an idea. How many super powered humans do you ever see in dark souls? Throughout all the games, the idea that we gain the power of a lord by killing so many dudes with massive souls is constant. Really, at least soul wise, by the time you reach Gael, you're a big shot. Your soul (which would be a dark soul since you're a human), must be substantial. A guy that's lost his mind, thirsting for a big fat dark soul, would be drawn to that.
Another more likely simple idea is that he needed the blood from the real first dark soul as pigment (which turned into him eating people when he saw that their blood ran dry), then went crazy. We already know he went crazy, he knew that would happen and left it to you to kill him and get his blood. Not unreasonable to assume in his madness, he would start going on a dark soul feeding frenzy.