dissecting the og module - where is the content type form submit handler for function og_ui_form_node_type_form_alter?
This happens automatically.

Adding a variable to that form means that it is automatically saved with variable_set() with a _node_type suffix. Similar to admin forms.

Here is another example: userpoints_nc_visits_form_node_type_form_alter().

As you can see, the form element is for example named userpoints_nc_visits_points and the default value is fetched with userpoints_nc_visits_points_type (inside the get setting api function).