No, not every aspect of their doctrine was fixated on eugenics and race. They killed millions of Catholics, homosexuals, communists, trade unionists and others, especially the extremely hybrid Gypsies, without regard to actual genetics. Hitler was not only not Aryan, but had Jewish ancestors - as did many if not most of the other Nazis pursuing genocide among other diabolical tyrannies.
Nazis cared about power. Race was a means to that end. Of course such means are part of the end, and Nazis did spend a lot of time on genocide and racist abuses and propaganda. But not because they actually cared about genetics as much as they cared about power.
Nationalism is properly defined simply as valuing one's nation extremely highly, typically devaluing any other nation to the extreme. A value that motivates competition with other nations that usually becomes violent, as there's no moral inhibition in harming "inferior" nations. The US is not at all alone in this, though its not usually as violent towards say France as it is towards say countries primarily inhabited by people who aren't White. You are correct in identifying some current US nationalism, but it goes even further: this week the Republican presidential candidate is embracing the rich idiot pushing the idea that the first Black president couldn't have been born in Hawaii, but must be a foreigner. Because that kind of racism is not just very popular in a large minority of Republicans, it's not rejected by the large majority of them. Obama must be Kenyan and inferior - nationalism in the service of racism. Not at all unique to the US.
Racism, nationalism and socialism are practiced more or less by many countries, and have been for centuries (and longer). They are not so simple as to be thrown around as if the Nazis define nationalism, racism, socialism, national socialism, or any other value system. The Nazis valued power above all, mainly the power to destroy as the power to control. They called themselves all kinds of things that they weren't, and all kinds of things they were that didn't really matter.
Most nationalist socialist governments have proven for generations they're not cataloging anyone for extermination. In fact they tend to be among the most accepting of diversity. And very specifically socialism is very different from fascism, even if they do have some configurations in common, like highly centralized government and economy . Nazis were the epitome of fascism, but called themselves socialists because socialism was popular and fascism wasn't.
The point is that if you're going to point out that genome sequencing is highly abusable by a government like the Nazis, just say "Nazis". Saying "nationalist socialists" just confuses the issue.