I would say that if you propose something we both agree is in both our interests, that's not manipulation. If you propose something that you feel is obviously in my best interest, but I resist doing it. If you coerce me into doing it, whether through preying on my greed, libido or fear, that's manipulative. Even if you tell yourself we're both clearly better off. Even if we're objectively better off by any metrics that make sense.
How can you coerce someone with greed or libido? Isn't coercion by definition the use of force or threats? Imagine someone tells you they were coerced into giving up a secret. When you ask how they were coerced, they say they were bribed, they were coerced through their greed. Wouldn't you say them accepting a bribe was totally voluntary, and calling it coercion would be inappropriate?
I think you are referring to the proposal at a different stage of the negotiation here than I was a moment ago. Let's consider the example with fixing the car from earlier.
Offer A: Fix my car for nothing.
As you say, if this offer is acceptable to both parties, there is no need for manipulation. Let's assume it isn't acceptable. I can use the fact that you want to drive my car as leverage, and use that to manipulate you into fixing my car. We can sum this up as a second offer.
Offer B: Fix my car, and I'll let you drive it.
Now, that offer might be so clearly acceptable to both parties that a roll seems unnecessary, if it's just completely obvious that you'd accept that. That doesn't mean manipulation hasn't occurred, it just means we didn't need a roll to resolve it. Suppose it's unclear whether it would work or not, and it would depend upon the finesse with which I made the offer, or brought to the surface your desire for the car. Then it might require a roll. Either way, if I successfully manipulate you into accepting the second offer, that must mean you believe you were better off accepting the offer than not. In other words, I'm not arguing that we were both better off with the first offer, clearly you didn't think so or manipulation would not have been necessary. But we could very well both agree that we are better off with the second offer. On the other hand, I could have taken a totally different approach.
Offer C: Fix my car, and I won't burn your house down.
You'd only take that offer if you thought it was better than not accepting it, but you certainly wouldn't say we both came away ahead on that deal.
I'd describe threats as social violence, but I wouldn't describe rewards that way. Manipulation includes both cases.
It might be useful to differentiate between the Manipulation move here, and the broader colloquial sense of the word manipulation. It seems like you reject that anything which doesn't isn't manipulation in the colloquial sense could fall under the Manipulation move. Now, we might have a hard time agreeing to the meaning of the word manipulation, but the Manipulation move seems to be defined reasonably clearly in the game text as the use of leverage to get someone to do what you want. I think there are cases where we can use leverage to get someone to do what we want, and thus the Manipulation move applies, but it could be debatable whether it's really manipulation in the usual sense of the word. Just like the Seizing by Force move doesn't always involve seizing anything, and acting under fire is very broadly interpreted and covers cases that you wouldn't call acting under fire outside the game.