The API calls return some javascript.
So when you make the following request:
https://abr.business.gov.au/json/AbnDetails.aspx?abn=74172177893&callback=callback&guid=myguid
It will return this:
callback({"Abn":"","AbnStatus":"","Acn":"","AddressDate":null,"AddressPostcode":"","AddressState":"","BusinessName":[],"EntityName":"","EntityTypeCode":"","EntityTypeName":"","Gst":null,"Message":"The GUID entered is not recognised as a Registered Party"})
This will invoke a function on the window object named callback, so somewhere in your code you have to define a function named callback which handles the call.
Here is an example of it being done for the request where callback=abnCallback, note the abnCallback function: https://abr.business.gov.au/json/Script/abnlookup-sample.js
Good luck, this doesn't really have anything to do with react btw. It's just a javascript thing.