Sure, here is a nice little presentation on the puzzle: https://rya.nc/forensic-bitcoin-cracking.html

The main discussion thread on the bitcoin forum is this but it has a low signal-to-noise ratio: https://bitcointalk.org/index.php?topic=1306983.0

There is a secondary thread here: https://bitcointalk.org/index.php?topic=5218972.0

The point of the puzzle is indeed to brute force some private keys (not public keys), but not all, as 2^256 is computationally impossible. The private keys that have been discovered so far have obviously many zeros in them, so in practice you are never going to accidentally steal from a legitimate address with actually 256 bits of entropy.

The creator of the puzzle is anonymous and never came forward (to my knowledge). The point of the puzzle is (1) to be a fun game, and (2) to be a publicly observable way of measuring current brute forcing capabilities.

First, a question: is there something similar for other blockchains? And, a clarification, when I said public keys I referred to public keys that match an unknown private key but I understand now (am I correct?) that this puzzle is purely brute forcing private keys with a lot of zeroes and then matching with the addresses in the blockchain (which would be a function from the public key).

I don't know if other blockchains have these puzzles. You are correct thas this puzzle is brute forcing private keys with a bunch of zeroes, from which a public key can be calculated.

Other bc's are centralized and don't need it as they can just revert or change their state.