How to check for Grouping field in Views submodule?
My question assumed that Views Datasource includes parent view format options such as grouping fields, but it does not. Rather than call all of the parent fields from the Views defaults, I copied only the field definition from views_plugin_style.inc to views_plugin_style_json.inc, within the options_form function.

The second part of my question was how to get the value of that field back out. It exists in $options["grouping"][$i]["field"], where $i is the Grouping Field Number, -1.

So, the value entered into "Grouping Field Nr.1" is $options["grouping"][0]["field"].