Hello Josh and welcome
When you purchase Template only and use it on a joomla website, you do not get all the extensions along with it as you ca see them in the demo showcase.
But since you are silver member, you are able to download the demo of the YouGames, and get your site to look exactly like the demo.
However if you already have a joomla installation, you can not use the demo installation there, so you would either delete previous installation (well if it was fresh one) and set this up insted, or make a subfolder on your server and move the files later.
Demo is installed just like joomla, it contains joomla files so no need to install joomla first.
Remember to install sample data in step 6
You are welcome to ask all you need here in the forum.