The Starmade-Starter is the launcher for downloading game files. The Starmade application by itself can't be run without it. You can find the download page for it here:
Once downloaded open up your web browser's downloads and place the Starmade-Starter in the location you would like the game to download your game files to (It's recommended you place it somewhere where administrator limitations do not take affect. Stay away from placing it on your desktop and in Program Files folders.) and run it. It should prompt you to download the game files. Afterwards you should be good to go!
If you don't feel like navigating to your Starmade installation folder to run the starter you can create a shortcut to the Starter on your desktop.