From what I have read (not having actually used Zulip) it always sounded like the chats were threaded in the same way that mailing lists or newsgroups are threaded.
That seems like a reasonable comparison. I've thought of Zulip as halfway between IRC and a forum.
No, it’s not fully threaded like those examples (or HN). In a particular discussion, you can’t reply to a post in the middle and have your reply branch off from the main discussion.