Are "non-mathematical" encryption algorithms comparably secure against brute force key recovery?
The premise of this question is flawed: There is no such thing as a "non-mathematical" cipher.
Every algorithmic procedure admits a mathematical description, hence is inherently mathematical in nature.



Besides that:

It is not hard to make primitives with massive key spaces, but that doesn't really achieve anything.
One can easily construct ciphers with $2^\text{gazillion}$ keys that are totally insecure.
This fallacy feels like a "freshman's converse" to Shannon's theorem: Perfect secrecy does imply big keys, but not the other way round!

The hard part of designing a good cipher is to make it small and fast while still achieving the desired security level.
The performance figures from the linked website are ridiculously slow according to modern standards.
Thus, even if that cipher is not broken — which I strongly doubt anyone has seriously studied — there is absolutely no reason to to prefer it over AES‑256.