I think there might be a miscommunication here somewhere.
1. You acknowledge that a person who rapes someone must have sociopathic tendencies, be driven by anger, sadism, or a desire to control others against their will.
2. That person, like most people, has sexual desires.
3. Therefore, their primary motivator for raping another person is the sexual desires and not their sociopathic tendencies? I honestly don't see how that follows.
To put it differently:
A and B both have sexual desires.
B is a sociopath while A isn't.
B commits rape while A doesn't.
In this case, what reason is there to assume that the shared trait between the two was the main motivator for rape rather than the trait which was not shared between them?