Actually, most of the games with custom chatrooms are just because they are put in the Multiplayer category. Also, the contact us link is incorrect. Here is the real link.
The Chat API is actually for games like Remnants of Skytone where players can talk to each other via the chat tab, not wasting space in the game. The chat tab is just a blank interface, no connection to Kongregate’s servers, AFAIK. So any multi-person interaction using the Chat API needs to be facilitated with your own server using the game you’ve made.