I would argue that the main thing that these areas have in common is that they are generally somewhat tropical or temperate. This, presumably, means that they had the kinds of climates that made food production possible.
This is not to say that all of these places have similar climates. The climate of the Eastern Seaboard of the United States is not very similar to the climate of New Guinea. However, we can note that these areas are all relatively close to the Equator. The Eastern US is probably the farthest from the Equator and it is relatively warm because of the effects of the Gulf Stream current.
Therefore, I would speculate that the crops mentioned in Table 5.1 were able to be domesticated because of the relatively benign climates of these regions. Of course, there were regional differences. New Guinea had very warm weather plants like sugar cane and bananas while the Andes had plants like potatoes that can thrive in drier and cooler climates. However, all of these areas were relatively close to the Equator and therefore had climates that were fairly conducive to agriculture.