This is intended behavior. Currently we do not render any GUIs nor do we have plans to do so.
I can't think of any practical workaround. Why do you need the chat in the rendered video?
The map has an ingame timer that he uses to keep track of the best times for the map, which displays in both the scoreboard and chat. I was using the mod so I didn't have to record every attempt I made before I got a good run, and was hoping for an easy way for him to verify the time. It shouldn't be too difficult for me to add a timer in myself later, it just turns into more work for him to verify.
