The Intelligence page states that "
at this level, many are capable of" achieving those four types of feat. They are four signs, not the only four possible qualifications in the way you're implying they are. If a character has one of those types of feats, then chances are, they qualify for Extraordinary Genius, but if they don't, then it doesn't necessarily mean they're blocked from getting the rank, even if they would only be at the baseline of the rank due to a lack of evidence.
The idea that Ayanokouji's intelligence rating should be decreased isn't self-evident. Ayanokouji is portrayed as a genius among geniuses whose intelligence surpasses what should be possible realistically, and he is knowledgeable about many important topics. This aligns with what the VS Battles Wiki identifies as an Extraordinary Genius: "Individuals whose knowledge spreads over multiple fields of science and who vastly surpass the real world's upper human limits." If I were familiar with
Classroom of the Elite, I would probably be able to explain it better, but I've seen discussions where his rank is called into question and I'm familiar with ranking intelligence enough for me to believe that his rank makes sense.