Simple JS XMLHttp wrapper class
I am concerned that you have added a layer of false generalization around a very specific, usually one-time use, request object.  I would think the class would be better named Request or similar to better clarify what this wrapper represents as currently stands. 

If your intent is to truly define a class that provides generalized request functionality ( get, post, put, etc.) then you should think more closely about how (and if) the class holds state for individual request objects. You probably would not store a common request object for every request on ‘this’, but rather would create a new request object for every method call.   If you find yourself no longer holding request state in your class, then you then would probably consider whether and instantiable class is really what you want. 

On a different front, your current code really does nothing to handle errors in the request. If you are spending the time to build a common request abstraction like this, you should add appropriate error handling. 

Finally, if you are in the business of building a new request abstraction, then I would strongly consider building of the much more modern and now widely supported Fetch API.