Any code that 100% conforms to supported versions of ECMAScript can be run in Chrome. But, you can't actually do anything useful in a browser with pure ECMAScript code because you can't interact with anything in the browser itself - instead you have to use browser-specific APIs to do that which are not ECMAScript methods, but browser-specific methods that are documented in different standards. Similarly, an ActionScript script likely interacts with its environment through non-ECMAScript methods which are not support in a browser.

And a new language that conforms to 100% to the latest version of ECMAScript would not have problems with the interpreter of each browser? I say this because every browser has a dedicated JavaScript interpreter or that's what I understand so far.

It's hard to tell what you're asking. There is no such thing as a new language that conforms to 100% of ECMAScript. That would just be an implementation of ECMAScript (not a new and different language) - just like each browser has its own implementation of ECMAScript. If it is indeed a new language, then it must have things in it that are not in ECMAScript. But, my point is that, pure ECMAScript code should run in any "compatible" ECMAScript implementation that is targeting the same ECMAScript version.

There are details of implementation that are not always complete in each browser since ECMAScript is a moving target (new revisions regularly) and the development on the implementation is ongoing work in each version. So, there can be compatibility issues around the edges of newish features, but that is true of any Javascript code running across browsers that is leverage very new features. Developers who are interested in good cross browser compatibility either stay away from the very latest features, cross compile their code to a lower common denominator using something like Babel or TypeScript or they study and test exactly what they can and can't use across all their target browsers.