Video game AI is made to mimic real human intelligence and create lifelike characters.

Generative ‚AI’ is just mumbo jumbo marketing talk for an algorithm that generates stuff from input.

The difference can be summed - The algorithm to generate responses can be used to create more believable game AI.

Do you get the difference? If something imitates a human then it is AI but a tool cannot be AI no more than wolfram alpha is.

If you use the algorithm and other tools to create a virtual person named Alice then this is attempt at AI. Alice is AI because it mimics real person