The script that the article author wrote wasn’t written in Airtable’s Scripting app. That’s a script that lives on another server and interacts with Airtable using the REST API.
You’re correct, the author left out a LOT of details, but I think the point of the article was just to show how little code is required to make it work, not to fully walk through the process. You would need to enlist the services of someone versed in web development to actually build something like the author describes. If you haven’t already done so, you might post in the “Hire a Consultant” category.