Please note that:
- in some (many? most?) places IQ tests does not include questions that require memorizing anything neither before or during the tests. (In I spoke to one colleague who was into such stuff and he made a major point out of the fact that asking for facts would disadvantage certain parts of the population.)
- Something is measured using such tests even if they don't contain math or facts, only sorting sequences or figuring out what elements fit in a sequence.
- We call that something "intelligence". We could call it something else: "Synthetic problem solving skill", "fu", or whatever, but we typically call it "intelligence".
- On average that "intelligence" also seems to be a good indicator for a persons performance in many situations. As far as I know chess playing benefits greatly.
- People who play chess will again and again end up in situations they haven't seen before and cannot have memorized.
- in those situations, the same skills that are measured in an intelligence test will help a person calculate outcomes and choose one to their advantage
Humans handle large data set with a cheat by using creativity and predictive reasoning to avoid having to store EVERY piece of data we encounter. Inference is a large part of this. Most models I'm aware of consider these traits to be related to intelligence.