I found this article to be rather muddled. It seems to be strongly implying that Hitler and the Nazis based their ideas on (a perversion of) Darwin’s writings, when there is apparently no evidence that Hitler read any of Darwin’s writings at all.
I also find the Darwin quote to be unfortunate, in that it stops after the first phrase of the opening sentence of this important paragraph:
The aid which we feel impelled to give to the helpless is mainly an incidental result of the instinct of sympathy, which was originally acquired as part of the social instincts, but subsequently rendered, in the manner previously indicated, more tender and more widely diffused. Nor could we check our sympathy, even at the urging of hard reason, without deterioration in the noblest part of our nature. The surgeon may harden himself whilst performing an operation, for he knows that he is acting for the good of his patient; but if we were intentionally to neglect the weak and helpless, it could only be for a contingent benefit, with an overwhelming present evil. We must therefore bear the undoubtedly bad effects of the weak surviving and propagating their kind; but there appears to be at least one check in steady action, namely that the weaker and inferior members of society do not marry so freely as the sound; and this check might be indefinitely increased by the weak in body or mind refraining from marriage, though this is more to be hoped for than expected.
It would be very hard for anybody who had read this to impute a viewpoint sympathetic to Nazism or ‘Social Darwinism’ to Darwin himself.