The only tree structured texting thing from back then that I remember is mailing list conversations. If you remember any names of old forums like that, it would be interesting to research. Maybe there are still screenshots or archived pages of those.

I believe old style means linear threads and other oldschool UI choices, not just look/aesthetics. That one has tree comment structure similar to all redditlikes, which (I believe) is relatively a recent invention? Have you seen comment trees like this few decades ago?