In this case the "arbitrary filter" was filtering applicants to a university for very basic math knowledge, so I think assuming that it's correlated with success at that university is not very far fetched.
I don't think after playing 20 or so levels I was much smarter for it. It turned out to be a bunch of rules that were extremely limited. You do begin to appreciate trig much more.
If you are being given a geometry subject test and are prepared for it, this is fair game. If the question is just given out of the blue as a brain teaser, then no, the university is not mining useful signals at all.
Either they can't be gamed, or they select for people who can at least be bothered to do the work to game them.