One thing I would improve with the authors article is he crammed a giant conditional statement on the http-method inside his one function. Serverless makes it easy to bundle a single function per HTTP method and even share common code between them. You can build out a whole application as a single npm package.
Bonuses include plugins for serverless that let you unit test your handlers, run a simulated APIG/Lambda/Dynamo environment locally for development, plugins that let you interact more deeply with AWS like assigning a custom domain to your APIG.
Example apps: https://github.com/serverless/examples