How does this object method definition work without the "function" keyword?

Solution 1:

How is it possible that this runs at all in any browser? Is is some sort of new ES6 functionality?

Yes.

...

Method definitions

A property of an object can also refer to a function or a getter or setter method.

var o = {
  property: function ([parameters]) {},
  get property() {},
  set property(value) {},
};

In ECMAScript 6, a shorthand notation is available, so that the keyword "function" is no longer necessary.

// Shorthand method names (ES6)
var o = {
  property([parameters]) {},
  get property() {},
  set property(value) {},
  * generator() {}
};

...

Solution 2:

ES6 allows "concise methods" which, as you've discovered, aren't cross-browser compatible yet.