As you’ve found, JavaScript doesn’t support operator overloading. The closest you can come is to implement toString (which will get called when the instance needs to be coerced to being a string) and valueOf (which will get called to coerce it to a number, for instance when using + for addition, or in many cases when using it for concatenation because + tries to do addition before concatenation), which is pretty limited. Neither lets you create a Vector2 object as a result. Similarly, Proxy (added in ES2015) lets you intercept various object operations (including property access), but again won’t let you control the result of += on Vector instances.
For people coming to this question who want a string or number as a result (instead of a Vector2), though, here are examples of valueOf and toString. These examples do not demonstrate operator overloading, just taking advantage of JavaScript’s built-in handling converting to primitives:
valueOf
This example doubles the value of an object’s val property in response to being coerced to a primitive, for instance via +:
Or with ES2015’s class:
Or just with objects, no constructors:
toString
This example converts the value of an object’s val property to upper case in response to being coerced to a primitive, for instance via +:
Or with ES2015’s class:
Or just with objects, no constructors: