IRC yes, chatbox, no. A chatbox just draws away from a user posting on your board, making conversation with others that can be viewed indefinitely, as opposed to a chatbox, which people would normally clear to keep loadtime on the board down.
Whilst a chatbox is normally used in other forums, I actually think this specific design doesn't require it, as quite honestly the posting is a live environment with instantaneous data shown. What you used to replicate with a chatbox, this software tends to me a more live chat environment than seen in any prior forum software. Not sure it even has a use in this software to be perfectly honest.
All you need is for new posts to load directly underneath your own post, and the entire forum is a chatbox in essence.