This is very interesting, thank you! When I was implementing random shuffling I used xoroshiro128+ instead of Mersenne twister and felt pretty good about it but only because it was used for randomness needed for Monte Carlo simulations, not for gambling games where there are potential adversaries looking to break it. Are you aware of how that one (xoroshiro128+) or other pseudo random generators fare against adversaries?

You're right that you wouldn't want to use any non-cryptographic PRNG for gambling games of any significant stake. Many low-stakes games will use them, relying on having many different players connected to one result source to protect themselves.

However, "624 consecutive outputs" is not the way to think about it, because those outputs are truncated to narrow integers. A single shuffled deck leaks about 230 bits of information, and backing out the state of a Mersenne twister needs several thousand bits of information.