Amazon goes to the extent to fully explain in the very first two sentences: "Serverless computing allows you to build and run applications and services without thinking about servers. With serverless computing, your application still runs on servers, but all the server management is done by AWS."
"Serverless" had no previous meaning - it's not like Amazon bastardized an existing term. The word will ultimately be defined once people expect it to mean something specific. Personally I like Amazon's use of the term here.
A recent similar example: the word "performant". The number of stubborn people who screamed "performant isn't a word!" was ridiculous. Everyone understands the intention behind the word "performant" without needing to have it explained to them. The introduction and wide adoption of a word is exactly how new words are folded into language. Language is fluid! Language has never been static and inflexible, and pouting because we have extended the dictionary over and over again for thousands of years is frivolous.