You said it, those tests are designed to measure human intelligence, because we know that there is a correspondence between test results and other, more general tasks - in humans. We do not know that such a correspondence exists with language models. I would actually argue that they demonstrably do not, since even an LLM that passes every IQ test you put in front of it can still trip up on trivial exceptions that wouldn't fool a child.

So they fail in their own way? They're not humans; that's to be expected.

An answer key would outperform the average human but it isn’t intelligent. Tests designed for humans are not appropriate to judge non humans.