All the apps created with Facebook Developers not categorized inside the "Games" category won't have the option "Invite friends" activated.
Follow these steps when you create a new app on Facebook Developers: Publishing a Facebook promo or tab with White Label
In this tutorial you can see where to select the "Games" category and the "Trivia & Word" subcategory when you create the app:
- Go to https://developers.facebook.com/
- We access the application that we need.
- In the section "Configuration-Basic Information" we find the following screen where we will change the category and subcategory.