When you ask an Amazon Alexa skill to do anything, it ultimately contacts another web server which executes code to process your request. This skill isn't any different, and needs such a server as well.
You have a few choices, ordered by difficulty:
Do note that while Heroku is the easiest to setup, it does lack some features, such as support for multiple installations of Kodi. If that is unimportant to you, we definitely recommend that you choose that deployment method.