Does the word "divorced" (طلاق) in this form, without any words before or after it, constitute a divorce if it was merely in response to a conversation with someone?

The word "talaq" (divorce) by itself does not constitute a divorce, because it is not a meaningful statement that entails a ruling. Rather, explicit divorce pronouncements must be directed to the wife, such as "I divorce you" (tallaqtuki) or "You are divorced" (anti taliq). Divorce does not occur if the word was not directed to the wife, or if it was a narration of someone else's speech.