I think it is better to show only Chat Rooms related to Web Application to the Web Application Chat Widget. Now it is showing all Chatrooms from http://chat.stackexchange.com/. Visitors may confused if all chatrooms are showing there.
I think some blending is good. Some of the rooms are not tied to a specific site, like the General Room, Sandbox, Chat Feedback to name a couple. Perhaps the sidebar could show rooms associated with the specific site and rooms that are not tied to a site?