is the chat area secure
What do you mean by that?
There is an option "Show player chat to spectators:" and I need to check if it requires all players to have it set or only one player for it to take effect.
Or are you asking if someone eavesdropping on your internet traffic can read what you write in the chat? I have idea if stream is encrypted.
want to make sure no one else can read chat
OK, I checked and if you set the option to "no" (either in the general options, or specifically for a table in the advanced options, see attached screenshots), spectators can't see what you (or the other players) type in the chat.