Never, never, ever underestimate the power of inertia.
In the instance you cite, of sex addiction vs compulsivity: the distinction is itself fairly new, and the use of the description to describe the patient has not yet stabilised, because the notion of compulsion as a medical condition has not been pervasive. So there’s a huge amount of inertia behind addiction, and an even huger amount of inertia because there hasn’t been until now a term for “one suffering from a compulsion”, to match “addict = one suffering from an addiction”.
If we went to Latin, we would use the past passive participle, find it to be compulsus (cf. addictus), and say that the person is a *compulse. But that hasn’t happened in English with any of the -pulse/-pel verbs. Not least because pulse and impulse as nouns are abstractions.
Since a sufferer of compulsion is grammatically one who is compelled, we could use *compelee. But compel and compulsion have actually diverged—compel is not used in the psychological context.
So, by accident, we don’t have a straightforward derivative word to describe such a patient. What to do, OP, what to do…
… actually this has already been solved. compulsive can be used as a noun to describe someone who exhibits a compulsive disorder: a sex compulsive. This is also something that English does with adjectives; cf. captive prisoner > captive. It sounds odd to us, because compulsive disorder describes the compeller and not the compellee; but it’s better than the alternatives, and it’s already in use.
The grammatical strangeness may slow down the take-up of compulsive; but if there is a compelling (ha!) case for a single word to be used for sufferers of compulsion, it will be taken up anyway.