I do not think number of API requests per month for $x is an accurate way to determine if $x is cheap or not. You are missing concurrency measurement. What was your highest requests per second on the sampled month?
Yes, I am not the author of the article though. I just shared it because I always wondered if Lambda was good enough for hobby projects and how much it would cost.
Generally, 2 million API calls per month will come around Max 10 requests per second (considering peak times as the requests will not be spread out evenly over time). Even a self-hosted $10 Digital Ocean instance could handle it with Node.js.
But the way the author has set up his application, getting started with highly available infrastructure with highly available DB with a possibility of 100 concurrent lambda executions is interesting. And one can get started with this in $11-$12 is very interesting indeed.
Didn't even notice the author when I posted it from my mobile. It's written by Eric Hammond. He was the guy who used to provide the Ubuntu AMIs in the early days of EC2.