Hitler was wrong. He erroneously believed that different human races exist at this day and age. That is not the case. All races, except for homo sapiens sapiens, are extince, the latest going extinct being the neanderthal race.
I know there are certain cultures that persist in calling ethnicities races, for example many people in the the USA. Even many educated Americans do that. And I guess it's a cultural thing; you guys don't have the same precise way of naming things as we do - by and large. But enough being off-topic...
DnD races are neither equal to human races, nor to human ethnicities. Races, by the biological definition, can procreate with one another. Dwarves and elves, by DnD's definition, can not procreate with one another. On top of that, the DnD writers may not have been overly concerned about science when they created a game where fall damage scales linearly, rapiers and maces penetrate full plate the same way etc.
Now this was my layman's perspective. Check out what actual scientists have to say, please: