It doesn't actually assume those facts - the study I linked to showed that empathy and logic cannot be active at the same time. Indeed, it concludes with the suggestion that healthy adults tend to cycle rapidly between the empathic and logical brain networks, and that pathologies like autism or Williams Syndrome occur when people get "stuck" in one neural network or the other.
It does have implications to how we might address poor math performance or poor social skills (if this theory is correct, which still isn't proven yet), notably by training people to recognize when one skillset is called for or the other, and encourage them to concentrate on the task at hand regardless of whether the other skillset may be more natural for them.
The study from the original post didn't find evidence of the E-S split. It's possible their SQ test was flawed. It's also possible practicing math causes your social skills to atrophy.
The conclusion of the authors could be accurate, but we definitely don't really know the whole picture yet.
It does have implications to how we might address poor math performance or poor social skills (if this theory is correct, which still isn't proven yet), notably by training people to recognize when one skillset is called for or the other, and encourage them to concentrate on the task at hand regardless of whether the other skillset may be more natural for them.