I didn't really clarify their system over there. (Can't wait for edit button if there's going to be one.) Well, on Kongregate they have chat moderators, then forum moderators. They have certain moderators assigned to each sub-forum they have there(the difference with their forum and AG's forum is that they assign different moderators to each sub-forum, while on AG all the current moderators can mod in every sub-forum, which is good.) They make users chat room moderators for basically the same reasons why AG makes users moderators. Chat moderators can go into any chat and have moderator powers there, they can silence/ban people. I'm not sure if they can kick there, but implementing kicking as a chat feature on AG will be good so that you don't have to jump straight to a ban/silence. With AG, there should be chat moderators like how Kongregate has them, but with a kicking feature. So, on AG it'll be: Having forum moderators and chat room moderators.
If that idea gets shot down by an administrator, then here's another:
Just letting users be able to create their own chat room on AG, being able to only let your friends enter the chat, and able to let anyone into your chat room. You'll have control over your chat room, being able to kick/ban/silence people on the chat room. Some flaws that I see with this is that what if people decide to abuse power within the chat room? What if not a lot of people will go into certain chat rooms because the owner of the room doesn't like them?
With those, they can be solved by a moderator of AG. But that'll take up a lot of time and the AG moderators will have a lot of things to be worrying about - chat rooms and forums. There will be a lot of chat rooms created, so I don't know how AG will keep track of those all. That's why I'd prefer the first idea that I presented.