I've always assumed claims like this are implying that average case code is written poorly and that's how It could be faster.
However as you point out we'd need all the assumptions made clear to believe such a claim.
In that case, they literally are writing JS and using a compiler to get JS that is faster than any normal handwritten JS would be. You could write your JS that way but it would be completely unreadable and unmaintainable.
In principle, it's always a certainty that JS can be written as performant as Dart, never just a possibility. The possibility part only comes in with respect how optimally the JS code is written.
The interesting part here is I think is how often does this happen? How often can significant improvements be made that would be impractical, or even unlikely for a developer to match?
This claim always bugged me. The output of dart2js is raw JS. Same with CoffeeScript (which makes a similar claim). So these claims are totally reliant on parameters that haven't been defined, ie. what constitutes "equivalent" handwritten code?