Omega used some concrete method to win his game, much in the same way that the fellow in question uses a particular method to win the punching game.

A crucial difference is that the punching game is real, while Newcomb's problem is fiction, a thought experiment.

In the punching game, you can try to learn how the trick is done and how to defeat the opponent, and you are still engaged in the punching game.

In Newcomb's problem, Omega is not a real thing that you could discover something about, in the way that there is something to discover about a real choshi dori master. There is no such thing as what Omega is really doing. If you think up different things that an Omega-like entity might be doing, and how these might be defeated to win $1,001,000, then you are no longer thinking about Newcomb's problem, but about a different thought experiment in some class of Newcomb-like problems. I expect a lot of such thinking goes on at MIRI, and is more useful than endlessly debating the original problem, but it is not the sort of thing that you are doing to defeat choshi dori.