What is the reason for the big divide in Brazil and Argentina? The blue parts have more indigenous descents, while yellow is predominantly European?

I think that it's less about direct descendants and more about cultural influence. For example, contrast the map in the OP with this one:

Sure, it kind of fits for the Northwest, but not for Patagonia - that has a rather large indigenous population and yet it's tan-coloured. Look also at Misiones: pretty much the opposite happens, it's blue in the map but your typical person there is an European descendant.

Same deal with Brazil, although African heritage is likely more typical than Amerindian heritage.