The striatum is rich in dopamine and D1 receptors, is adjacent to the nucleus accumbens (the primary pleasure center), and is involved in movement control (and is therefore lacking dopamine in the case of Parkinson's disease).
I have learned that the striatum is also largely responsible for sexual pleasure. Furthermore, it's sex-related function is dependent upon input from serotoninergic neurons. I therefore conclude that PSSD is the result of damage to these serotoninergic neurons in the striatum, and consequent lack of dopamine release to the sex-related neurons of the striatum, and in turn, the lack of sex-related pleasure in the nucleus accumbens. The fact that there is a direct effect upon the striatum, and only an indirect effect upon the nucleus accumbens, also explains why sexual pleasure is effected by PSSD, whereas other types of pleasure (such as that of food) remain intact.
That lack of dopamine release in the striatum need not cause any Parkinsons-like symptoms, nor are such symptoms reported, because Parkinsons-like dystonia could only result from depleting dopamine from the striatum beyond it's basal level that is required for movement control. Unless a person could somehow tap this basal dopamine and use it for the sexual system, Parkinsons-like symptoms should not occur.