It took me a couple reads of the PDF but I think you're right. The author creates an HTTP request Promise, and then immediately returns a response thereby shutting down the Lambda. They have logging which shows the background HTTP request was in the early stages of being sent to the server but the server never receives anything. They also have an error handler that is supposed to catch errors during the HTTP request but it isn't executed either. The reason for both seems quite obvious: it's completely expected that a Lambda being shutdown wouldn't finish making the request and it certainly wouldn't stick around to execute error handling code after the request was cancelled.
As an aside I find it strange that the author spent all this time writing this document but would not provide the actual code that demonstrates the issue. They say they wrote "minimal plain NodeJS functions" to reproduce it. What would be the reason to not show proof of concept code? Instead they only show code written by an AWS engineer, with multiple caveats that their code is different in subtle ways.
The author intends for this to be some big exposé of AWS Support dropping the ball but I think it's the opposite. They entertained him through many phone calls and many emails, and after all that work they still offered him a $4000 account credit. For comparison, it's implied that the Lambda usage they were billed for is less than $700 as that figure also includes their monthly AWS Support cost. In other words they offered him a credit for over 5x the financial cost to him for a misunderstanding that was his fault. On the other hand, he sounds like a nightmare customer. He used AWS's offer of a credit as an admission of fault ("If the platform functioned correctly, then why offer credits?") then got angry when AWS reasonably took back the offer.