That's a BIG topic, but I can point to a few things. Caveat emptor: I have a very strange set of beliefs about philosophy of science that makes some people mad.
We could inspect the idea of "solving" something. It's my impression that mathematicians have a very different approach to what it means to solve things than, say, most scientists do. At least their language and demeanor about it tends to be very different. I think most mathematicians aren't very concerned, for instance, if their proof maps onto the physical world, because math is inherently abstract, etc. (It may have implications for the physical world, but it very quickly becomes science or something other than math--art and occultism spring to my mind, in fact--when you start thinking that way.)
And this process of solution that the game describes, seems very aesthetic to me, especially in the advanced variant. What criteria, what impulse, what set of beliefs inform what processes you use to go about solving something? Similarly, what criteria inform your declaration of the problem being solved/finished? These are, I would argue, essentially aesthetic criteria. I have seen so many mathematicians (my physicist ex among them) who prize elegance and beauty in proofs above all else. I have known mathematicians who have found a perfectly "functional" proof, who then go on off in search of another, more aesthetically pleasing one, or a more interesting one, or some other arbitrary--aesthetic--requirement.
The truth is that there cannot be one, singular set of criteria for proof. Any given paradigm requires input from Outside (there's that word again) against which to judge its own set of assumptions and practices. My normal example is the so-called "Scientific Method," which doesn't functionally exist in any meaningful way. If it did, science wouldn't be able to do anything. (For more on this, I recommend Against Method, Paul Feyerabend. I do not especially recommend Kuhn, but to each their own.) And I argue that the same is true for any functional tradition of knowing (art, occultism, whatever): it does not, cannot exist in a vacuum. All progress happens across worldviews, inter-paradigmatically. There's no objective Aristotelian Platform from which to inspect ourselves and our belief systems, there are only other belief systems. And the belief systems that acknowledge this, the way that art and occultism and some approaches to math and science do, are stronger and more agile and more functional as a result.
And this game implicitly acknowledges that, I think. First, randomizing methodologies is a way of getting Outside (of your personal paradigm, of the prevailing paradigm of your culture of inquiry), of reaching for something beyond the current set of possibilities. And once that becomes a natural thing, you can remove the randomness and allow your burgeoning aesthetic judgment to guide that process. And once you've mastered that, you can apply those techniques and proclivities in other areas (such as solving this game). All of this points to an approach to knowledge acquisition that's open and syncretic, that allows input from other, inherently incommensurable ways of knowing.
So that's not a lot of specifics about parallels to art and occultism, but I think it gestures at a larger point?