You ALMOST get it, but then entirely missed the point.
You need to demonstrate that the test is consistent with a business necessity. If you have a large enough people who have taken the test, and enough data on how they perform, you can make that demonstration. You've got the data, and it is enough to cover the military despite people like you who think that it "doesn't actually test intelligence or problem-solving abilities." Because, whatever it actually tests, it predicts real world performance well enough to pass legal muster.
The US military is the only organization that I'm aware of which has an IQ test with enough data that they can pass legal muster. Very specifically I'm talking about the AFQT, which is the core of the ASVAB. See https://www.military.com/join-armed-forces/asvab details on the ASVP. And see https://asvabmilitarytest.com/asvab-compared-other-iq-tests to see that it really is an IQ test to tell if you're smart enough to be in the military. And not just whether you can join, but which jobs inside of the military they will allow you to pursue.
The military has documented that this is an effective way to find people who can do things like fill out paperwork properly, and follow orders in the field. The reason why other businesses can't do the same is not because the test is useless, but because they don't have the data to demonstrate how useful the test actually is.