Unlike Karl Marx's economic theory of history's "haves" and "have-nots", what is Diamond's thesis about these two groups in Guns, Germs, and Steel?
The answer to this question can be found in Chapter 5 of Guns, Germs, and Steel. A good formulation of Diamond’s thesis can be found on p. 103 of the paperback edition of the book (the last page of the chapter). There, Diamond tells us that
The peoples of areas with a head start on food production thereby gained a head start on the path leading toward guns, germs, and steel.
What Diamond is saying is that having a “head start of food production” made a society into “haves” while not having this head start made them into “have-nots.”
What Diamond is claiming in this book is that food production (farming) leads to the development of technology and of epidemic diseases. Technology and epidemic diseases allowed some peoples to go out and conquer other peoples. Food production does this because it allows people to live together in dense, permanent communities. In such communities, there are many people, some of whom will be able to invent and create technology. In such communities, it is easier for epidemic diseases to survive.
Thus, what Diamond is saying is that living in an area that is good for agriculture makes a society become a “have” while not living in such an area makes a society a “have-not.”
As mentioned in the terrific answer above and before mine, the ones who gained the most advantage in the economy were the ones who had initial direct access to food production. Being able to produce and grow through an agricultural view, those individuals were able to essentially get a head start on those who did not. This is what Diamond is referring to in regards to these two groups that you inquired about.