The influence of Dart on ES6 and 7 apart from SIMD (John McCutchan shout-out, John did the Dart work and then worked on https://github.com/johnmccutchan/ecmascript_simd; I had some small helpful role to do with the project involving Mozilla and Intel, too) and the courage and validation -- not the idea, which pre-dates Dart -- of giving the for (let...) loop a binding per iteration in ES6 as in Dart, there has been no influence or help from Dart.
Modules in ES6 have nothing to do with Dart, and the work started in 2010, well before Dart ("Dash") leaked. Classes too pre-date Dart, in some ways they go back to JS2/ES4 of the 1999-2003 era, and ES4 of the 2006-8 era.
CoffeeScript owes a lot to Ruby and Python, of course, and I did design-champion fat arrow functions into ES6, inspired in part by CoffeeScript. ES6's for-of loop is responding to the same gravity-well as CoffeeScript's for-of, but it differs in substantial aspects. And so on.
Languages influence one another -- news at 11 -- but Dart did very little intentional uplift work for JS. SIMD is the big and very good exception to this norm. Better late than never, I say. Now is a good time to help get value objects including bignums into ES7.