It's not their own definition, this was the default definition just a few years ago.
People started to use the term for something else and now it became the main meaning.
"Serverless" is nowadays "AWS Lambda" (and similar products).
I wish people called it FaaS (function as a service), but they call it "serverless", and it's fine I guess
1. Per invocation billing 2. No need to provision resources ahead of time
Taking AWS's example
1. EC2 is not serverless but Lambda is 2. RDS is not serverless but Aurora Serverless is.