The JavaScript output runs on all of those browsers, but only Chrome (or actually the special "Dartium" version of Chrome) has a VM to run Dart code directly.
Dart brings improvements to the language and tools that are worthwhile regardless of the VM being available in the user's client. dart2js is the primary method of deploying Dart code, and there's nothing bad about that.
Most of them's tool support does not even compare to Dart. Dart code can run directly in Browser for the starters, multiple strong IDEs, sane debugging and modularity support.
He said "for development". The nice thing about the VM in Dartium is that you don't need to compile as part of your development workflow until you need to QA and deploy, just edit and refresh. You don't need the VM in consumer browsers to get that benefit.