It's a hard problem because "AI" has been a term since the 50s but has been used to describe different approaches to making a computer do things over time. The way game developers use "AI" to mean "hardcoded logic for game behavior" is fully inline with what "AI" meant in the 60s when they were using symbolic AI to write the first computer-controlled chess games.
Then AI programmers hit the wall of hard-coded logic, went through an AI winter, and what survived on the other end was logic that was automatically trained from big data sets. We used to call that "machine learning" because "AI" had connotations of snake oil from previous AI winters. But then within the past decade, tech companies with grandiose ambitions decided that "machine learning" was too nerdy so resurrected "AI" to refer to LLMs and their ilk.
The term is just a muddled mess.