you modified mdcClassNames twice

controllers.application.js

import Ember from 'ember';

export default Ember.Controller.extend({
  appName: 'Ember Twiddle'
});

templates.application.hbs

<h1>You modified "mdcClassNames" twice</h1>
<br>
<br>
{{outlet}}
<br>
<br>

<div class="">
  {{mdc-checkbox
  }}
</div>

twiddle.json

{
  "version": "0.13.0",
  "EmberENV": {
    "FEATURES": {}
  },
  "options": {
    "use_pods": false,
    "enable-testing": false
  },
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.3/jquery.js",
    "ember": "2.16.2",
    "ember-template-compiler": "2.16.2",
    "ember-testing": "2.16.2",
    "ember-material-components-web": "^0.0.37"
  },
  "addons": {
    "ember-data": "2.16.3"
  }
}