So far the response to the suggestion of adding a native Dart runtime to anything other than Chromium proper has been extremely negative. WebKit didn't want it, Mozilla doesn't seem to want it. Maybe Opera will include it since they're using Blink?
It may not be a Microsoft feature but it's basically being treated the same as one. Native Client is getting similar treatment.
Dart is the language and the Dart VM and dart2js are implementations. That's an important distinction. Dart, via dart2js, does run on all modern browsers.
Sorry, by 'currently' I meant current plans, you're absolutely right.
I think it's pretty likely that Opera might include it, and that could change things - even though their marketshare tends to be kind of small they've traditionally had some power in terms of boosting adoption of new tech.
It may not be a Microsoft feature but it's basically being treated the same as one. Native Client is getting similar treatment.