JS and Game

That sounds reasonable to me. I've used both constructor functions and factory functions. Objects are great at encapsulating related things together - into what other languages might call a class. Whichever you choose shouldn't matter much - perhaps there are performance differences? may be worth testing at https://jsperf.com/. Other than that, main difference is in the use - or absence of - the this keyword.

// constructor function
var Dog = function() {
  // private properties
  var sound = "woof!";

  // public methods
  this.speak = function() { console.log(sound); }
}

// factory function
var Cat = function() {
  // private properties
  var sound = "meow!";

  // the returned object can be thought of as the object's API
  return {
    speak: function() { console.log(sound); }
  }
}

var peanut = new Dog();
peanut.speak(); // "woof!";
peanut.sound; // undefined

var grumpy = Cat();
grumpy.speak(); // "meow!"
grumpy.sound; // undefined

You are somewhat correct in that a good approach is to create everything as objects.

However with the enemies, you could have one main enemy class, and then different types of subclasses which extend the main enemy class, which detail enemies with different properties and methods. Then you could create new instances of those classes within your script.