I agree with you. I agree it's valuable work. I totally disagree with their claim.
A better analogy is: someone who's never taken the AIME might think "there are an infinite number of math problems", but in actuality there are a relatively small, enumerable number of techniques that are used repeatedly on virtually all problems. That's not to take away from the AIME, which is quite difficult -- but not infinite.
Similarly, ARC-AGI is much more bounded than they seem to think. It correlates with intelligence, but doesn't imply it.
> but in actuality there are a relatively small, enumerable number of techniques that are used repeatedly on virtually all problems
IMO/AIME problems perhaps, but surely that's too narrow a view for all of mathematics. If solving conjectures were simply a matter of trying a standard range of techniques enough times, then there would be a lot fewer open problems around than what's the case.
Maybe I'm misinterpreting your point, but this makes it seem that your standard for "intelligence" is "inventing entirely new techniques"? If so, it's a bit extreme, because to a first approximation, all problem solving is combining and applying existing techniques in novel ways to new situations.
At the point that you are inventing entirely new techniques, you are usually doing groundbreaking work. Even groundbreaking work in one field is often inspired by techniques from other fields. In the limit, discovering truly new techniques often requires discovering new principles of reality to exploit, i.e. research.
As you can imagine, this is very difficult and hence rather uncommon, typically only accomplished by a handful of people in any given discipline, i.e way above the standards of the general population.
I feel like if we are holding AI to those standards, we are talking about not just AGI, but artificial super-intelligence.