Strange. Now I saw the chatrooms in the sidebar on MO (main site) when viewing a question. I have tried several questions (with many answers) on Mathematics and Academia - on the main site I do not see chatrooms. On meta I see them.

Probably I should wait a bit to see whether the fact that they are now shown on MO is due to recent changes related to ads (in fact, no ads). Or whether this will persist - and at least on MO they will be shown also on the main site.