In JavaScript engines that support ECMAScript 2015 (aka ES6) class syntax, this can be accomplished using the new.target meta-property:

function Node() {
   if (new.target === Node) throw TypeError("new of abstract class Node");
}

or using class syntax:

class Node {
   constructor () {
      if (new.target === Node) throw TypeError("new of abstract class Node");
   }
}

in either case, just define AttributionalNode as:

class AttributionalNode extends Node {
   constructor () {
      super();
   }
   setAttr(attr) {
      this.atText = attr;
   }
}

new Node();               // will throw TypeError
new AttributionalNode();  // works fine

For a more detailed explanation of new.target see section 4.2 of this document.

This would work:

function Node() {
    if (this.constructor === Node) {
        throw new Error("Cannot instantiate this class");
    }
}

function AttributionalNode() {
    Node.call(this); // call super
}

AttributionalNode.prototype = Object.create(Node.prototype);
AttributionalNode.prototype.setAttr = function (attr) {
    this.atText = attr;
};
AttributionalNode.prototype.constructor = AttributionalNode;

var attrNode = new AttributionalNode();
console.log(attrNode);
new Node();

Note: you cannot refer to this.prototype inside the constructor, as the prototype is only a property of the constructor function, not of the instances.

Also, see here for a good article on how to properly extend JS classes.

Adapting @levi's answer, you can go with a similar solution for using with ES6 today (as new.target isn't established yet):

You can see it running on Babel's repl: http://bit.ly/1cxYGOP

class Node {
    constructor () {
      if (this.constructor === Node) 
          throw new Error("Cannot instantiate Base Class");
    }

    callMeBaby () {
      console.log("Hello Baby!");
    }
}

class AttributionalNode extends Node {
  constructor () {
    super();
    console.log("AttributionalNode instantiated!");
  }
}

let attrNode = new AttributionalNode();
attrNode.callMeBaby();

let node = new Node();