Words often have multiple meanings. The “engineering” in “prompt engineering“ is like in “social engineering”. It’s a secondary, related but distinct meaning.
For example, Google defines the second meaning of "engineering" as:
2. the action of working _artfully_ to bring something about. "if not for his shrewd engineering, the election would have been lost"
Look up “engineering” in almost any dictionary, and it will list something along those lines as one of the meanings of the word. It is a well-established, nontechnical meaning of “engineering”.
Your posted definitions contradict your conclusion - I would argue there is nothing calculated (as parent poster said, there is no calculation, it just trying and watching what works), artful or skillful (because it's so random, what skill is there to develop?) about "prompt engineering".
For example, Google defines the second meaning of "engineering" as:
2. the action of working _artfully_ to bring something about. "if not for his shrewd engineering, the election would have been lost"
(https://www.google.com/search?q=define%3AEngineering)
Merriam-Webster has:
3 : calculated manipulation or direction (as of behavior), giving the example of “social engineering”
(https://www.merriam-webster.com/dictionary/engineering)
Random House has:
3. skillful or artful contrivance; maneuvering
(https://www.collinsdictionary.com/dictionary/english/enginee...)
Webster's has:
The act of maneuvering or managing.
(https://www.yourdictionary.com/engineering)
Look up “engineering” in almost any dictionary, and it will list something along those lines as one of the meanings of the word. It is a well-established, nontechnical meaning of “engineering”.