Final answer:
Deleting a Hangouts conversation from your list only removes your copy; the other participants will still see the conversation until they delete it themselves.
Step-by-step explanation:
When you delete a Hangouts conversation on your end, it's true that the conversation remains visible to the other participants until they also choose to delete it from their Hangouts list. Communication platforms like Hangouts are designed to ensure that each user has control over their own chat history, but not that of others. So, when you delete a chat, you're only removing your copy of the conversation; the other person will retain their copy unless they also decide to delete it.