Thank you for your answer.
The other party in question quoted from "The Ohio State Bar":
"Minors do not have full rights to enter into contracts. If a minor enters into a contract with an adult, the minor has the option to either honor or cancel the contract before he or she complies with the terms of (or performs) the contract. By complying with the terms, the minor is acting in a way that honors the contract, so the contract will be binding on the minor as well as the adult. If a minor chooses to cancel a contract because he or she is not 18 years of age, the minor should take action to cancel the contract before becoming 18. However, a minor cannot cancel a contract if the cancellation would cause an unfair result, or allow the minor to benefit from his or her own wrongdoing. For example, a minor cannot purchase a car, wreck it, then cancel the contract and expect not to have to pay for the car.
Finally, in some situations, a minor can enter into a binding contract and not have the right of cancellation. These situations generally involve contracts for necessaries such as good, clothing, shelter and medical care. The minor's parents may be held liable on contracts for necessaries. Contracts for medical care raise special questions and are addressed below."
It could be seen that my running a new website that is very similar to the one I did work for can bring about an "unfair result." In addition, it states that if a minor does hold his part of the contract, it is no longer voidable. I did perform my duties in the contract.