It is actually Beez that is showing the custom output. We do not use custom html overrides in our templates, that ensures that the output is always done by Joomla itself. Therefore our template is not controlling this functionality, at all.
I have a brand new Joomla install setup locally, with all the demo data preinstalled. I have setup a new Category List menu item and set it to show all Sub Categories. This is what that looks like using the default Prostar template:
You can see that Incline produces the exact same layout (different styling):
So you can see our templates our using the exact layout that Joomla outputs with no changes. Beez is different because they have actually included a custom com_content override in the template, which we never do. This is what the latest Beez template looks like:
That is closer to what you have above, but that is only because that template has custom outputs which override the default Joomla layout. If you rename the folder:
That means the override will not be called anymore, and when you do that, it's back to the default Joomla output:
You mentioned in your other post:
"A little help seemed to be to insert a folder "/templates/incline/html/com_content/category/" with a "default_children.php""
There should not be any overrides for com_content in html folder for Incline. We do not use overrides, nor do we include in any the download. If you have overrides there you are overriding the output of Joomla. We do not use overrides in com_content so that Joomla is always outputting the layout, and never the template.
If you want, you can copy the override from Beez3 to Incline, but I would highly recommend against this. Overrides cause a lot of problems with backwards compatibility, ie: any updates to com_content will not be included because hey are over-written. That is why we do not use them, and there is no need for them.
From all my tests and, the screenshots I've provided above, our templates are not controlling the output of this layout. You are comparing the default layout of Joomla to two other templates that use custom com_content overrides.