This post claims that
All modern chatting interfaces, without exception, implement a hierarchical and a not-chronological schema for chat.
It also links another post which gives an example schema for such an interface. Basically, each message contains a reference to the message it replies to (the parent). In order to display a conversation, those references are traversed recursively, starting from messages without a parent.
But I don't see how this is any better than simply sorting the messages by the time they were sent. Since one person may send multiple messages in a row, this doesn't save me from identifying the author (even if it's just a boolean). Can somebody explain the advantages?