ECMA standards are supported not by the websites that are served up inside of browsers, but by the browsers themselves.
For a list of which browsers support what (in terms of ECMA 6) please see: ECMAScript 6 compatibility table
Additionally, this is also the case for CSS standard support. You can find if a particular CSS tag / function is supported by your browser at https://caniuse.com/
*Edit* I suppose that I should add that while there are all sorts of neat little additions to the newest standard. I can't think of too much that can't be done in the older version. If there is something in particular in the new version that you'd like the use, the exception being the syntactical sugar like fat arrows (=>) for functions, I'm sure we can figure out a way to accomplish it.