I'm not sure that is the case, because of the native Dart VM.
CoffeeScript compiles very straightforwardly into JS, with similar performance to normal JS. But Dart is significantly different, and the Dart VM could be faster than Dart-compiled-to-JS, both because (1) The Dart VM will be optimized for Dart in new ways, and (2) It isn't clear that Dart code will be extremely efficient when compiled to JS.
So CoffeeScript adoption needs no support from browser vendors, but Dart, if it is to fulfill its goal of being fast, might need the Dart VM. And that does need browser vendor support.
Natively run Dart will (otherwise, what's the point) than the JS it can be compiled into. What I forsee is some kind of conditional that will allow Chrome to run the Dart code, and other browser get served the compiled-into-JS.
Demanding an extension installation is a no-go.