I don’t know that much about the subject, but the rapist typology used by the FBI doesn’t classify rapists according to their level of sexual desire. The four main types of rapist in the FBI typology are “power-reassurance”, “power-assertive”, “anger-retaliatory”, and “anger-excitation”. (See this interview with FBI profiler Roy Hazelwood for more about what this actually means.) Sexual desire is a significant factor for all except the anger-retaliatory rapist, but either power or anger is considered the primary motivation for all four major categories. There are also two secondary categories described in the interview, the opportunistic rapist and the gang rapist.
The FBI system was apparently developed largely by Hazelwood, and is based on the work of psychologist Nicholas Groth. It looks like Groth was one of the first to make the claim that rape is not motivated primarily by sexual desire. He considered power, anger, and sadism the primary motives for rape, with power being the most common of the three.
I’d never heard of Groth until today when I was looking this stuff up, but I’m guessing the catchphrase “Rape isn’t about sex, it’s about power” was inspired by his work. I don’t know that Groth ever used those exact words, but it seems to be his idea (or at least one that he was an early advocate of). His book Men Who Rape: The Psychology of the Offender was published in 1979 and would likely have been of interest to second-wave feminists, so that may how the catchphrase originated. This is just my speculation though, I haven’t been able to trace the history of the phrase.*
The FBI system is the rapist typology I’ve seen referenced the most before in popular sources and self-defense literature, but a little searching in PsychINFO indicates that the Massachusetts Treatment Center Rapist Typology, Version 3 (MTC:R3) may be preferred by psychological researchers today. The MTC:R3 recognizes four primary motivations for rape: opportunity, pervasive anger, sexual gratification (sadistic or non-sadistic), and vindictiveness. I don’t think these are meant to be mutually exclusive, I gather that a rapist could be classified under the MTC:R3 as being motivated by any combination of these things.
I didn’t turn up any other motivation-based rapist typologies, but I wouldn’t be surprised if others did exist. The above comes from an hour or two on Google and in PsychINFO, so it’s hardly exhaustive. All the other classification systems for rapists I turned up were based on their behavior rather than their motives, perhaps because it’s a lot easier to establish what a rapist did than it is to figure out what a rapist was thinking.
*It sometimes appears as “Rape isn’t about sex, it’s about violence”, which I would take to be not a claim about the motivation for rape but rather a statement about how society should view rape. I’m not sure which form of the catchphrase came first.