The receipt of a gift concludes the act/transaction of giving. There is no give-backs, except when a gift is not just a gift, and that is when something is expected in return. In such a case, the donative intent is missing, the giver does not just intend on leaving the gift with the receiver.
The engagement ring is a conditional gift. It is given upon the condition that a marriage will follow. If there is no marriage, the condition is not satisfied, and the ring should return to the donor.
As opposed to the birthday gift scenario, the giving of the engagement ring is not the start of the act of giving. The engagement process starts with a question, will you marry me? Only upon an affirmative answer, yes, do you give an engagement ring.
In some states, you can argue that if the giver broke off the engagement, the ring need not be returned, but Illinois views this as impractical. Who broke off the engagement is nearly impossible to prove (imagine, a party calling off the wedding as their promised-one was caught with someone else, who is responsible?).
In Illinois, if the condition of marriage is not met, the ring goes back, in nearly every instance... unless it cannot be located, of course.