There are 3 reasons why sexual abuse can play a strong role in sexual addiction later on in life.
1) The abuse leaves emotional scars that remain in the person's subconscious for life. Such a person may feel pain deep down, making them more prone to using "self-medicating" behaviors that help sooth their inner pain.
2) When a person is abused, they are helpless and lack control over their circumstances. Later in life, this person may attempt to assert "control" by sexually acting-out by themselves. Subconsciously, they are seeking to regain a feeling of "control" over what they felt was out of their control, by using the same behavior that was done to them. (This is also why many abused tragically become abusers themselves).
3) As we can see in the excerpt below, early exposure to any drug makes the user much more at risk. The sexual abuse exposed the victim to sexuality prematurely.
From an article on Retorno.com, re - the risk factors of addiction:
Individuals who are predisposed to addiction, impulsivity, compulsivity, depression or anxiety – usually thanks to a combination of genetic and environmental influences – have added risk and need to be extremely careful.
Studies show that genetic factors can increase or decrease the risk for addiction, usually by altering the ways in which a particular substance or activity is experienced in the body and brain. Genetic makeup also plays into many psychiatric disorders, including depression, anxiety and bipolar disorder, among others. And it's well-known that individuals dealing with these emotionally painful issues often choose to compulsively “self-medicate” with an addictive substance or behavior.
Nevertheless, genetics are not entirely to blame. In fact, research indicates that environmental factors are equally at play. For instance, if someone was neglected or abused in childhood their risk of addiction jumps, just as it does if they were exposed to addictive substances or behaviors early in life. (The younger a person is when he or she first uses an addictive substance or starts an addictive behavior, the greater the risk of developing an addiction.) So it appears that most addicts become addicted thanks to a convergence of risk factors – typically a mixture of genetic predisposition, poor parenting and early exposure to the drug and its effects.