Hello @aexaexx,
We actually are not clear what you exactly meant by the comment box but if you are referring to the Contact form as you see in the contact page of the demo then at first you need to activate the contact form 7 plugin.
https://wordpress.org/plugins/contact-form-7/
Activate the plugin and create the contact form by going to Admin Panel > Contact > Add new.
Now copy the shortcode generated into the content edit screen of the Contact page.
Screenshot:
http://prntscr.com/jkla9i
Hope this helps.
Let us know if you have any issues further.
Thank you.
Best Regards!!