> You don’t test each new human to see if they have it

We do, its called school and we label some humans with different learning disabilities. Some of those learning disabilities are grave enough that they can't learn to do tasks we expect humans to be able to learn, such humans can be argued to not posses the general intelligence we expect from humans.

Interacting with an LLM today is like interacting with an Alzheimer patient, they can do things they already learned well but poke at it and it all falls apart and they start repeating themselves, they can't learn.

Yes, there are diseases, injuries, etc. which can impair a human’s cognitive abilities. Sometimes those impairments are so severe that we don’t consider the human to be intelligent (or even alive!). But note that we still make this distinction without anything close to a rigorous formal definition of general intelligence.