Yes, all of this is basically correct. However, it is also basically the same in the original Newcomb although somewhat more intuitive. In the original problem Omega decides to put the one million or not depending on its estimate of what you will do, which likely depends on "what kind of person" you are, in some sense. And being this sort of person is also going to determine what kind of decision theory you use, just as the gene does in the genetic version. The original Newcomb is more intuitive, though, because we can more easily accept that "being such and such a kind of person" could make us use a certain decision theory, than that a gene could do the same thing.
Even the point about other people knowing the results or using certain reasoning is the same. If you find an Omega in real life, but find out that all the people being tested so far are not using any decision theory, but just choosing impulsively, and Omega is just judging how they would choose impulsively, then you should take both boxes. It is only if you know that Omega tends to be right no matter what decision theory people are using, that you should choose the one box.
I am currently learning about the basics of decision theory, most of which is common knowledge on LW. I have a question, related to why EDT is said not to work.
Consider the following Newcomblike problem: A study shows that most people who two-box in Newcomblike problems as the following have a certain gene (and one-boxers don't have the gene). Now, Omega could put you into something like Newcomb's original problem, but instead of having run a simulation of you, Omega has only looked at your DNA: If you don't have the "two-boxing gene", Omega puts $1M into box B, otherwise box B is empty. And there is $1K in box A, as usual. Would you one-box (take only box B) or two-box (take box A and B)? Here's a causal diagram for the problem:
Since Omega does not do much other than translating your genes into money under a box, it does not seem to hurt to leave it out:
I presume that most LWers would one-box. (And as I understand it, not only CDT but also TDT would two-box, am I wrong?)
Now, how does this problem differ from the smoking lesion or Yudkowsky's (2010, p.67) chewing gum problem? Chewing Gum (or smoking) seems to be like taking box A to get at least/additional $1K, the two-boxing gene is like the CGTA gene, the illness itself (the abscess or lung cancer) is like not having $1M in box B. Here's another causal diagram, this time for the chewing gum problem:
As far as I can tell, the difference between the two problems is some additional, unstated intuition in the classic medical Newcomb problems. Maybe, the additional assumption is that the actual evidence lies in the "tickle", or that knowing and thinking about the study results causes some complications. In EDT terms: The intuition is that neither smoking nor chewing gum gives the agent additional information.