Hi Mollie,
1. Parameter Group refers to Custom Form Sections, so that's unrelated to your current challenge.
2. Display Order refers to the order in which the Parameter Options are listed. 1 is first, 2 is second, etc.
To my knowledge there is no API endpoint or syntax that will alphabetize the Parameter Options for you. In the UI, checking that box while editing a dropdown field reorders the list using JavaScript, not an API call. The API call that is sent to Workfront when saving the custom form informs Workfront that it should set a new order for the Parameter Options of the dropdown field, but it's not a simple "alphabetize this list" command - it says "set the display order of Alpha to 1. set the display order of Beta to 2. set the display order of Charlie to 3." and so on.
To do this action via API, your script or scenario that is sending the API command to Workfront should POST the new Parameter Options, then GET them all from the Parameter, then use its own logic to alphabetize the list, then set the new display order values accordingly, then PUT those updates with the new display order back to Workfront .
Honestly it's probably not worth the amount of effort needed to code the function, unless you need to do this to hundreds of fields.

If anyone knows a secret unpublished endpoint that performs this action, I'm interested to know it!