String.prototype.toJadenCase = function () { // no argument
  //...
};

Your method is called like this here: str.toJadenCase() and in Run.js your're calling it like this: str.toJadenCase(str) or like this: String.toJadenCase(str)

Read this, I hope it helps.

I'm not sure what you mean by not using prototype. I copied my code into Run.js and called the function and it does exactly what the expected output is so I don't know why it's failing here.

Not a kata issue, a problem with your code, use Question label for things like this. You're not using prototype ok, it doesn't use an argument.