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:

If you have already created your app without realizing these changes, you can change the category and subcategory on the "App Details" section:

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