I don't understand how you can argue that gaming provides a real benefit, but AI doesn't.
If gaming's benefit is entertainment, why not acknowledge that AI can be used for the same purpose?
There are other benefits as well -- LLMs can be useful study tools, and can help with some aspects of coding (e.g., boilerplate/template code, troubleshooting, etc).
If you don't know what they can be used for, that doesn't mean they don't have a use.