Thanks for the link to additional info. I’ve read the list a few more times, and it seems that at the top of the list it says:
The following APIs are fully or partially supported.
But then, since under ‘extension’ it says that “only” getBackgrondPage and getUrl are supported, I would assume it means that chrome.extension.sendMesssage is not supported. Is this just a glitch in the documentation? The developer.mozilla page you linked to seems to indicate that message passing is indeed a primary way extensions will work.