Unable to enable “Thumbnail Settings” functionality

I have two installations of WordPress 4.5.3. One is using a theme developed by a third party for a client. In this theme, images uploaded do NOT have the “Thumbnail Settings” option available.

This is what I’m getting:

This is what I want and this works in another install of 4.5.3 with a default theme:

So I am under the impression this is a matter of a theme setting. How do I enable the Thumbnail Settings feature?

Here is my Stack Exchange question: http://wordpress.stackexchange.com/q/251677/7739

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