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"

(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”.