Why is it correct the phrase: "Wie wichtig ist den Deutschen dieser Sport" and not "Wie wichtig ist dem Deutschen dieser Sport"?
Both is correct; but your assumption about accusative is wrong.
It is dative in both cases. "den Deutschen" is dative of plural "die Deutschen". So the first sentence is translated as "How important is this sport for the Germans (for German people)?"
In the second sentence you talk about a single male person or about a prototypical German regardless of genders (so in the same meaning as the plural) - How important is this sport for the German? There are not so many situations where you could use this sentence but still it is correct.
4I partly disagree with the last paragraph. It does not necessarily refer to only males but could be used to refer to a prototypical German no matter the gender. It has to be clear from the context though, that you are talking about Germans in general. Otherwise, good answer. Jul 26, 2017 at 15:25
@problemofficer Yes, you're right. I added this.– EllerJul 26, 2017 at 15:36
I took the liberty to propose an edit to specifically mention the genders to make the explanation clearer. I also removed the reference to me. Thank you, but it decreases readability. Jul 26, 2017 at 15:43