If you go here while logged in as your domain's admin account
https://chrome.google.com/webstore/developer/dashboard/
You can add a new app. After you upload the zip file that contains your manifest.json and your .png thumbnail, you can set the required screenshots, language, set it that it's not a public app and only available to your domain.
After everything is good with the app, you can get it's app/item ID by clicking on "more info"
ex: idapdbjamincgfjilegbblamaekdkhdk
Now you'll need to get back to the admin console for your domain.
*Make sure to select the OU of users that you want this applied to
Let me know if you end up having further difficulty or questions.